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A015224 Even pentagonal pyramidal numbers. 5
0, 6, 18, 40, 126, 196, 288, 550, 726, 936, 1470, 1800, 2176, 3078, 3610, 4200, 5566, 6348, 7200, 9126, 10206, 11368, 13950, 15376, 16896, 20230, 22050, 23976, 28158, 30420, 32800, 37926, 40678, 43560, 49726, 53016, 56448, 63750, 67626, 71656 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

Eric Weisstein's World of Mathematics, Pentagonal Pyramidal Number

Index entries for linear recurrences with constant coefficients, signature (1, 0, 3, -3, 0, -3, 3, 0, 1, -1).

FORMULA

From Ant King, Oct 24 2012: (Start)

a(n) = a(n-1) +3*a(n-3) -3*a(n-4) -3*a(n-6) +3*a(n-7) +a(n-9) -a(n-10).

a(n) = 3*a(n-3) -3*a(n-6) +a(n-9) +192.

Sum_{n>=0} 1/a(n) = log(2)/2 + Pi/4 + 5*Pi^2/24 - 2 - C = 0.27217..., where C is Catalan’s constant (A006752).

G.f.: 2*x*(3+6*x+11*x^2+34*x^3+17*x^4+13*x^5+11*x^6+x^7) / ((1-x)^4*(1+x +x^2)^3). (End)

a(n) = A002411(A004772(n+1)). - Bruno Berselli, Oct 24 2012

MATHEMATICA

LinearRecurrence[{1, 0, 3, -3, 0, -3, 3, 0, 1, -1}, {0, 6, 18, 40, 126, 196, 288, 550, 726, 936}, 40] (* Ant King, Oct 19 2012 *)

PROG

(PARI) x='x+O('x^30); concat([0], Vec(2*x*(3+6*x+11*x^2+34*x^3 +17*x^4 +13*x^5+11*x^6+x^7)/((1-x)^4*(1+x +x^2)^3))) \\ G. C. Greubel, Aug 24 2018

(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(2*x*(3+6*x+11*x^2+34*x^3+17*x^4+13*x^5+11*x^6+x^7)/((1-x)^4*(1+x +x^2)^3))); // G. C. Greubel, Aug 24 2018

CROSSREFS

Cf. A002411, A014800, A015223, A014799, A006752.

Sequence in context: A023658 A059834 A299263 * A163983 A191829 A023620

Adjacent sequences: A015221 A015222 A015223 * A015225 A015226 A015227

KEYWORD

nonn,easy

AUTHOR

Mohammad K. Azarian

EXTENSIONS

More terms from Patrick De Geest, Jul 14 1999

STATUS

approved

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Last modified December 3 07:15 EST 2022. Contains 358512 sequences. (Running on oeis4.)