A030279 COMPOSE squares with squares.

1, 8, 50, 276, 1397, 6672, 30565, 135668, 587426, 2493056, 10407393, 42848800, 174348417, 702245128, 2803634370, 11106624804, 43697519013, 170871040752, 664492915061, 2571316718500, 9905232077842, 38000679280352, 145240335213857, 553203971301184, 2100403987129441, 7951405959127848

Offset: 1

Author

Christian G. Bower

Keywords

• nonn
• nice
• easy

Links

• N. J. A. Sloane, Transforms
• Index entries for linear recurrences with constant coefficients, signature (12, -54, 115, -132, 108, -59, 24, -6, 1).

Crossrefs

Cf. A000290, A030267, A279282.

Programs

Mathematica

CoefficientList[Series[((1-x)^3(1+x)(1-2x+4x^2-x^3))/((1-4x+2x^2-x^3)^3),{x,0,30}],x] (* or *) LinearRecurrence[{12,-54,115,-132,108,-59,24,-6,1},{1,8,50,276,1397,6672,30565,135668,587426},30] (* Harvey P. Dale, Mar 14 2016 *)

PARI

Vec(((1-x)^3*(1+x)*(1-2*x+4*x^2-x^3))/((1-4*x+2*x^2-x^3)^3)+O(x^66)) \\ Joerg Arndt, Apr 21 2013

Formula

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

a(n) = 12*a(n-1)-54*a(n-2)+115*a(n-3)-132*a(n-4)+108*a(n-5)-59*a(n-6)+24*a(n-7)-6*a(n-8)+a(n-9). - Wesley Ivan Hurt, Apr 23 2021