Revision History for A325677
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing all changes.
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#9 by Susanna Cuyler at Tue May 14 22:07:16 EDT 2019
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#8 by Gus Wiseman at Mon May 13 19:03:49 EDT 2019
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#7 by Gus Wiseman at Mon May 13 19:02:42 EDT 2019
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| EXAMPLE
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Andand the following compositions:
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#6 by Gus Wiseman at Mon May 13 19:01:03 EDT 2019
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| COMMENTS
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Also the number of length-k compositions of n such that every restriction to a subinterval has a different sum. A composition of n is a finite sequence of positive integers summing to n.
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#5 by Gus Wiseman at Mon May 13 16:06:14 EDT 2019
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| CROSSREFS
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Cf. A000079, A007318, A103295, A108917, A143823, A325676, A325679, A325687.
Cf. A325676, A325677, A325679, A325683, A325687.
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#4 by Gus Wiseman at Mon May 13 16:05:14 EDT 2019
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| CROSSREFS
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Rightmost column is A325683.
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#3 by Gus Wiseman at Mon May 13 12:52:12 EDT 2019
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#2 by Gus Wiseman at Mon May 13 12:51:56 EDT 2019
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| NAME
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allocatedIrregular triangle read by rows where T(n,k) is the number of Golomb rulers of length n forwith Gusk + 1 Wisemanmarks, k > 0.
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| DATA
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1, 1, 1, 2, 1, 2, 1, 4, 1, 4, 2, 1, 6, 6, 1, 6, 8, 1, 8, 18, 1, 8, 16, 1, 10, 30, 4, 1, 10, 34, 14, 1, 12, 48, 28, 1, 12, 48, 42, 1, 14, 72, 76, 1, 14, 72, 100, 1, 16, 96, 160, 8, 1, 16, 98, 190, 8, 1, 18, 126, 284, 40, 1, 18, 128, 316, 70
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| OFFSET
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1,4
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| COMMENTS
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Also the number of length-k compositions of n such that every restriction to a subinterval has a different sum.
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| LINKS
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Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GolombRuler.html">Golomb Ruler.</a>
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| EXAMPLE
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Triangle begins:
1
1
1 2
1 2
1 4
1 4 2
1 6 6
1 6 8
1 8 18
1 8 16
1 10 30 4
1 10 34 14
1 12 48 28
1 12 48 42
1 14 72 76
1 14 72 100
1 16 96 160 8
1 16 98 190 8
1 18 126 284 40
1 18 128 316 70
Row n = 8 counts the following rulers:
{0,8} {0,1,8} {0,1,3,8}
{0,2,8} {0,1,5,8}
{0,3,8} {0,1,6,8}
{0,5,8} {0,2,3,8}
{0,6,8} {0,2,7,8}
{0,7,8} {0,3,7,8}
{0,5,6,8}
{0,5,7,8}
And the following compositions:
(8) (17) (125)
(26) (143)
(35) (152)
(53) (215)
(62) (251)
(71) (341)
(512)
(521)
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| MATHEMATICA
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DeleteCases[Table[Length[Select[Join@@Permutations/@IntegerPartitions[n, {k}], UnsameQ@@ReplaceList[#, {___, s__, ___}:>Plus[s]]&]], {n, 15}, {k, n}], 0, {2}]
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| CROSSREFS
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Row sums are A169942.
Row lengths are A325678(n) = A143824(n + 1) - 1.
Column k = 2 is A052928.
Column k = 3 is A325686.
Cf. A000079, A007318, A103295 cmplt_rul, A108917, A143823.
Cf. A325676, A325677, A325679, A325683, A325687.
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| KEYWORD
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allocated
nonn,tabf
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| AUTHOR
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Gus Wiseman, May 13 2019
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| STATUS
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approved
editing
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#1 by Gus Wiseman at Mon May 13 09:12:36 EDT 2019
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| NAME
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allocated for Gus Wiseman
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| KEYWORD
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allocated
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| STATUS
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approved
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