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A283551
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a(n) = -1 + 5*n/6 + n^3/6.
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2
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-1, 0, 2, 6, 13, 24, 40, 62, 91, 128, 174, 230, 297, 376, 468, 574, 695, 832, 986, 1158, 1349, 1560, 1792, 2046, 2323, 2624, 2950, 3302, 3681, 4088, 4524, 4990, 5487, 6016, 6578, 7174, 7805, 8472, 9176, 9918, 10699, 11520, 12382, 13286, 14233, 15224, 16260
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OFFSET
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0,3
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COMMENTS
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a(n) - a(-n) = 2*a(n) + 2 = A033547(n).
(a(n+10) - a(n-10))/10 = 36, 35, 36, 39, 44, 51, ... .
a(n) is in the fifth line of
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, ...
16, 11, 7, 4, 2, 1, 1, 2, 4, 7, 11, 16, 22, 29, ...
-26, -15, -8, -4, -2, -1, 0, 2, 6, 13, 24, 40, 62, 91, ...
31, 16, 8, 4, 2, 1, 1, 3, 9, 22, 46, 86, 148, 239, ...
etc.
First line: A000004. Second line: A000012. Third line: (from 0) A001477 and (backwards) -A001477. Fourth line: (from the second 1 and from the first 1) A000124(n). Fifth line: (from -1) a(n) and -A000125(n). Sixth line: (from 3) A223718, (from the first 1) A000127(n), the second 1 is a separatrix. For the sixth, eighth and tenth lines, Ron Hardin found A223718(n), A223659(n), A225011(n).
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LINKS
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FORMULA
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a(-n) = - a(n) - 2 = -1, -2, -4, -8, -15, -26, -42, ... = -A000125(n).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 3.
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EXAMPLE
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G.f. = -1 + 2*x^2 + 6*x^3 + 13*x^4 + 24*x^5 + 40*x^6 + 62*x^7 + ... - Michael Somos, Jul 07 2022
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MAPLE
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MATHEMATICA
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CoefficientList[ Series[(2x^3 -4x^2 +4x -1)/(x -1)^4, {x, 0, 50}], x] (* or *)
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PROG
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CROSSREFS
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Essentially a duplicate of A003600.
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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