A193008 -id:A193008 - cp's OEIS frontend

A193041 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.

0, 1, 3, 13, 44, 122, 292, 631, 1267, 2411, 4408, 7820, 13560, 23109, 38867, 64721, 106964, 175782, 287660, 469275, 763795, 1241071, 2014128, 3265848, 5292144, 8571817, 13879587, 22468981, 36368252, 58859186, 95251828, 154138015

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Clark Kimberling, Jul 15 2011

nonn
easy

The titular polynomials are defined recursively: p(n,x)=x*p(n-1,x)+1+n^3, with p(0,x)=1. For an introduction to reductions of polynomials by substitutions such as x^2->x+1, see A192232 and A192744.

Index entries for linear recurrences with constant coefficients, signature (5,-9,6,1,-3,1).

Cf. A192232, A192744, A192951, A193008.

Mathematica
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(See A193008.)
```

a(n) = 5*a(n-1)-9*a(n-2)+6*a(n-3)+a(n-4)-3*a(n-5)+a(n-6).

G.f.: -x*(7*x^2-2*x+1)/((x-1)^4*(x^2+x-1)). [Colin Barker, Nov 12 2012]

cp's OEIS Frontend

A193041 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.

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