A279284 Self-composition of the pentagonal numbers; g.f.: A(x) = G(G(x)), where G(x) = g.f. of A000326.

0, 1, 10, 74, 469, 2662, 14115, 71360, 348143, 1652200, 7669883, 34969286, 157060011, 696514465, 3055404733, 13277356490, 57222978070, 244831062184, 1040760406476, 4398642943496, 18493603597214, 77388169532299, 322451025667910, 1338291853544522, 5534486308363461, 22812231761335189, 93741611639348947, 384122032722040412

Offset: 0

Author

Ilya Gutkovskiy, Dec 09 2016

Keywords

• nonn
• easy

Links

• N. J. A. Sloane, Transforms
• Eric Weisstein's World of Mathematics, Pentagonal Number
• Index to sequences related to polygonal numbers
• Index entries for linear recurrences with constant coefficients, signature (12,-51,91,-75,66,-28,15,-3,1).

Crossrefs

Cf. A000326, A030279, A030280.

Programs

Mathematica

CoefficientList[Series[x (1 - x)^3 (1 + 2 x) (1 - x + 7 x^2 - x^3)/(1 - 4 x + x^2 - x^3)^3, {x, 0, 25}], x]
LinearRecurrence[{12, -51, 91, -75, 66, -28, 15, -3, 1}, {0, 1, 10, 74, 469, 2662, 14115, 71360, 348143}, 26]

Formula

G.f.: x*(1 - x)^3*(1 + 2*x)*(1 - x + 7*x^2 - x^3)/(1 - 4*x + x^2 - x^3)^3.

a(n) = 12*a(n-1) - 51*a(n-2) + 91*a(n-3) - 75*a(n-4) + 66*a(n-5) - 28*a(n-6) + 15*a(n-7) - 3*a(n-8) + a(n-9).