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A192955 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments. 3
0, 1, 2, 7, 18, 41, 84, 161, 294, 519, 894, 1513, 2528, 4185, 6882, 11263, 18370, 29889, 48548, 78761, 127670, 206831, 334942, 542257, 877728, 1420561, 2298914, 3720151, 6019794, 9740729, 15761364, 25502993, 41265318, 66769335, 108035742 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

LINKS

Table of n, a(n) for n=0..34.

Index entries for linear recurrences with constant coefficients, signature (4,-5,1,2,-1).

FORMULA

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

G.f.: -x*(-1+2*x-4*x^2+x^3) / ( (x^2+x-1)*(x-1)^3 ). - R. J. Mathar, May 08 2014

a(n)-a(n-1) = A192954(n-1). - R. J. Mathar, May 08 2014

MATHEMATICA

(See A192954.)

CROSSREFS

Cf. A192232, A192744, A192951, A192955.

Sequence in context: A051743 A054111 A295054 * A055503 A077802 A095151

Adjacent sequences:  A192952 A192953 A192954 * A192956 A192957 A192958

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jul 13 2011

STATUS

approved

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Last modified February 20 20:55 EST 2019. Contains 320345 sequences. (Running on oeis4.)