Revision History for A114121
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#52 by Michael De Vlieger at Wed Apr 10 08:46:48 EDT 2024
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#51 by Seiichi Manyama at Wed Apr 10 07:35:22 EDT 2024
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#50 by Seiichi Manyama at Wed Apr 10 01:21:41 EDT 2024
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| FORMULA
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a(n) = [x^n] 1/((1-2*x) * (1-x)^(n-1)). - Seiichi Manyama, Apr 10 2024
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| STATUS
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approved
editing
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#49 by Susanna Cuyler at Sun Jun 27 07:52:08 EDT 2021
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#48 by Gus Wiseman at Sun Jun 27 06:18:02 EDT 2021
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#47 by Gus Wiseman at Sun Jun 27 06:17:54 EDT 2021
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| CROSSREFS
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A344610 counts partitions by sum and positive reverse-alternating sum.
A344616 lists the alternating sums of partitions by Heinz number.
Cf. A000041, A000070, A000302, A000346, A003242, A027306, A032443, A058622, A058696, A119899, A239830, A344607, A344610.
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#46 by Gus Wiseman at Sun Jun 27 00:12:36 EDT 2021
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| CROSSREFS
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The case of alternating sum > 0 appears to be A000302.
The case of alternating sum <= 0 is A000302.
Cf. A000041, A000070, A000302, A000346, A003242, A027306, A032443, A058622, A058696, A119899, A239830, A344607.
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#45 by Gus Wiseman at Sun Jun 27 00:11:09 EDT 2021
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| FORMULA
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For n > 0, a(n) = 2^(2n-1) - A008549(n). - Gus Wiseman, Jun 27 2021
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| CROSSREFS
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The case of alternating sum < 0 appears to beis A008549.
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#44 by Gus Wiseman at Fri Jun 25 21:52:29 EDT 2021
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| COMMENTS
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Also the even bisection of A116406 = number compositions of 2nn with alternating sum >= 0, which iswhere the even bisection of A116406. The alternating sum of a sequence (y_1,...,y_k) is Sum_i (-1)^(i-1) y_i. The a(3) = 26 compositions are:
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#43 by Gus Wiseman at Mon Jun 21 02:29:47 EDT 2021
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| CROSSREFS
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Cf. A000041, A000070, A000097, A000346, A003242, A006330, A027306, A028260, A032443, A058622, A058696, A119899, `A138364, A239830, `A294175, ~A344604, A344605, A344607 ptns_sats_wkpos, `A344618, A344650, A344739.
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