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A269428
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Alternating sum of heptagonal pyramidal numbers.
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1
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0, -1, 7, -19, 41, -74, 122, -186, 270, -375, 505, -661, 847, -1064, 1316, -1604, 1932, -2301, 2715, -3175, 3685, -4246, 4862, -5534, 6266, -7059, 7917, -8841, 9835, -10900, 12040, -13256, 14552, -15929, 17391, -18939, 20577, -22306, 24130, -26050, 28070
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..40.
OEIS Wiki, Figurate numbers
Eric Weisstein's World of Mathematics, Pyramidal Number
Eric Weisstein's World of Mathematics, Heptagonal Pyramidal Number
Index entries for linear recurrences with constant coefficients, signature (-3,-2,2,3,1).
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FORMULA
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G.f.: x*(1 - 4*x)/((x - 1)*(x + 1)^4).
a(n) = ((20*n^3 + 42*n^2 + 4*n - 9)*(-1)^n + 9)/48.
a(n) = Sum_{k = 0..n} (-1)^k*A002413(k).
Sum_{n>=1} 1/a(n) = -0.8939139178060972723185724267951741... . - Vaclav Kotesovec, Feb 26 2016
E.g.f.: (9*sinh(x) - (33*x - 51*x^2 + 10*x^3)*exp(-x))/24. - Franck Maminirina Ramaharo, Nov 11 2018
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MATHEMATICA
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Table[((20 n^3 + 42 n^2 + 4 n - 9) (-1)^n + 9)/48, {n, 0, 40}]
LinearRecurrence[{-3, -2, 2, 3, 1}, {0, -1, 7, -19, 41}, 41]
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PROG
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(Magma) [((20*n^3+42*n^2+4*n-9)*(-1)^n+9)/48: n in [0..50]]; // Vincenzo Librandi, Feb 26 2016
(PARI) a(n)=((20*n^3 + 42*n^2 + 4*n - 9)*(-1)^n + 9)/48 \\ Charles R Greathouse IV, Jul 26 2016
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CROSSREFS
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Cf. A000292, A002413, A002717, A173196, A266677.
Sequence in context: A195349 A160422 A213782 * A097240 A097241 A067889
Adjacent sequences: A269425 A269426 A269427 * A269429 A269430 A269431
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KEYWORD
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sign,easy
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AUTHOR
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Ilya Gutkovskiy, Feb 26 2016
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STATUS
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approved
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