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A193007
Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.
1
0, 1, 1, 9, 36, 108, 268, 591, 1201, 2303, 4232, 7534, 13096, 22357, 37649, 62749, 103772, 170616, 279300, 455747, 741905, 1205651, 1956816, 3173114, 5142096, 8329033, 13486753, 21833361, 35339796, 57195108, 92559292, 149781399, 242370481
OFFSET
0,4
COMMENTS
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.
FORMULA
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*(2*x^4-6*x^3+13*x^2-4*x+1)/((x-1)^4*(x^2+x-1)). [Colin Barker, Nov 12 2012]
MATHEMATICA
(See A193006.)
LinearRecurrence[{5, -9, 6, 1, -3, 1}, {0, 1, 1, 9, 36, 108}, 40] (* Harvey P. Dale, Sep 13 2021 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 14 2011
STATUS
approved