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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

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).

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.)