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A245300
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Triangle T(n,k) = (n+k)*(n+k+1)/2 + k, 0 <= k <= n, read by rows.
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5
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0, 1, 4, 3, 7, 12, 6, 11, 17, 24, 10, 16, 23, 31, 40, 15, 22, 30, 39, 49, 60, 21, 29, 38, 48, 59, 71, 84, 28, 37, 47, 58, 70, 83, 97, 112, 36, 46, 57, 69, 82, 96, 111, 127, 144, 45, 56, 68, 81, 95, 110, 126, 143, 161, 180, 55, 67, 80, 94, 109, 125, 142, 160, 179, 199, 220
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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FORMULA
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T(2*n, n) = A062725(n) (central terms).
T(n, n-7) = (-1)*A147973(n), n >= 7.
T(n, n-10) = A222182(n-4), n >= 10.
T(2*n, n-1) = A081270(n-1), n >= 1.
T(2*n, n+1) = A117625(n+1), n >= 1. (End)
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EXAMPLE
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First rows and their row sums (A245301):
0 0;
1, 4 5;
3, 7, 12 22;
6, 11, 17, 24 58;
10, 16, 23, 31, 40 120;
15, 22, 30, 39, 49, 60 215;
21, 29, 38, 48, 59, 71, 84 350;
28, 37, 47, 58, 70, 83, 97, 112 532;
36, 46, 57, 69, 82, 96, 111, 127, 144 768;
45, 56, 68, 81, 95, 110, 126, 143, 161, 180 1065;
55, 67, 80, 94, 109, 125, 142, 160, 179, 199, 220 1430;
66, 79, 93, 108, 124, 141, 159, 178, 198, 219, 241, 264 1870;
78, 92, 107, 123, 140, 158, 177, 197, 218, 240, 263, 287, 312 2392.
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MATHEMATICA
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Table[k + Binomial[n+k+1, 2], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Apr 01 2021 *)
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PROG
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(Haskell)
a245300 n k = (n + k) * (n + k + 1) `div` 2 + k
a245300_row n = map (a245300 n) [0..n]
a245300_tabl = map a245300_row [0..]
a245300_list = concat a245300_tabl
(Magma) [k + Binomial(n+k+1, 2): k in [0..n], n in [0..15]]; // G. C. Greubel, Apr 01 2021
(Sage) flatten([[k + binomial(n+k+1, 2) for k in (0..n)] for n in (0..15)]) # G. C. Greubel, Apr 01 2021
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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