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A270694 Alternating sum of centered heptagonal pyramidal numbers. 1
0, -1, 8, -23, 51, -94, 157, -242, 354, -495, 670, -881, 1133, -1428, 1771, -2164, 2612, -3117, 3684, -4315, 5015, -5786, 6633, -7558, 8566, -9659, 10842, -12117, 13489, -14960, 16535, -18216, 20008, -21913, 23936, -26079, 28347, -30742, 33269 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

More generally, the ordinary generating function for the alternating sum of centered k-gonal pyramidal numbers is -x*(1 - (k - 2)*x + x^2)/((1 - x)*(1 + x)^4).

LINKS

Ilya Gutkovskiy, Table of n, a(n) for n = 0..500

OEIS Wiki, Centered pyramidal numbers

Index entries for linear recurrences with constant coefficients, signature (-3,-2,2,3,1).

FORMULA

G.f.: -x*(1 - 5*x + x^2)/((1 - x)*(1 + x)^4).

a(n) = -3*a(n-1) - 2*a(n-2) + 2*a(n-3) + 3*a(n-4) + a(n-5).

a(n) = ((-1)^n*(2*n + 1)*(14*n^2 + 14*n - 9) + 9)/48.

E.g.f.: (1/48)*(9*exp(x) - (9 + 66*x - 126*x^2 + 28*x^3)*exp(-x)). - G. C. Greubel, Mar 28 2016

MATHEMATICA

LinearRecurrence[{-3, -2, 2, 3, 1}, {0, -1, 8, -23, 51}, 39]

Table[((-1)^n (2 n + 1) (14 n^2 + 14 n - 9) + 9)/48, {n, 0, 38}]

PROG

(PARI) x='x+O('x^100); concat(0, Vec(-x*(1-5*x+x^2)/((1-x)*(1+x)^4))) \\ Altug Alkan, Mar 21 2016

(MAGMA) [((-1)^n*(2*n + 1)*(14*n^2 + 14*n - 9) + 9)/48 : n in [0..40]]; // Wesley Ivan Hurt, Mar 21 2016

CROSSREFS

Cf. A004126 (centered heptagonal pyramidal numbers).

Cf. A000330, A006323 (partial sums of centered heptagonal pyramidal numbers), A019298, A232599.

Sequence in context: A175346 A225280 A218711 * A027054 A048467 A002765

Adjacent sequences:  A270691 A270692 A270693 * A270695 A270696 A270697

KEYWORD

easy,sign

AUTHOR

Ilya Gutkovskiy, Mar 21 2016

STATUS

approved

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Last modified February 24 05:37 EST 2018. Contains 299597 sequences. (Running on oeis4.)