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 A269428 Alternating sum of heptagonal pyramidal numbers. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS 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). FORMULA 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 MATHEMATICA 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] PROG (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 CROSSREFS Cf. A000292, A002413, A002717, A173196, A266677. Sequence in context: A195349 A160422 A213782 * A097240 A097241 A067889 Adjacent sequences: A269425 A269426 A269427 * A269429 A269430 A269431 KEYWORD sign,easy AUTHOR Ilya Gutkovskiy, Feb 26 2016 STATUS approved

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Last modified February 2 06:25 EST 2023. Contains 360000 sequences. (Running on oeis4.)