A192469 Coefficient of x in the reduction by x^2->x+3 of the polynomial p(n,x)=1+x^n+x^(2n).

2, 8, 44, 224, 1178, 6200, 32786, 173600, 919988, 4877072, 25858754, 137115440, 727074530, 3855471416, 20444603516, 108412922240, 574888887530, 3048505597160, 16165538467442, 85722217226576, 454565670533252, 2410459729834544

Offset

1,1

Comments

For an introduction to reductions of polynomials by substitutions such as x^2->x+3, see A192232.

Links

Table of n, a(n) for n=1..22.

Formula

Empirical G.f.: -2*x*(x-1)*(3*x-1)/((3*x^2+x-1)*(9*x^2-7*x+1)). [Colin Barker, Nov 12 2012]

Example

The first four polynomials p(n,x) and their reductions are as follows:
p(1,x)=1+x+x^2 -> 4+2x
p(2,x)=1+x^2+x^4 -> 16+8x
p(3,x)=1+x^3+x^6 -> 61+44x
p(4,x)=1+x^4+x^8 -> 304+224x.
From these, read
A192468=(4,16,61,304,...) and A192469=(2,8,44,224,...)

Mathematica

(See A192468.)

Crossrefs

Cf. A192232, A192468.

Sequence in context: A264565 A018985 A018986 * A128656 A208044 A362413

Adjacent sequences: A192466 A192467 A192468 * A192470 A192471 A192472

Keyword

nonn

Author

Clark Kimberling, Jul 01 2011

Status

approved