A192468 -id:A192468 - cp's OEIS frontend

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

Clark Kimberling, Jul 01 2011

nonn

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

			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,...)

Cf. A192232, A192468.

Mathematica
```
(See A192468.)
```

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]

A192470 (A192469)/2.

Original entry on oeis.org

1, 4, 22, 112, 589, 3100, 16393, 86800, 459994, 2438536, 12929377, 68557720, 363537265, 1927735708, 10222301758, 54206461120, 287444443765, 1524252798580, 8082769233721, 42861108613288, 227282835266626, 1205229864917272

Offset: 1

Clark Kimberling, Jul 01 2011

nonn

See A192469.

Cf. A192469.

Mathematica
```
(See A192468.)
```

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

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Formula