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A193047 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments. 1
0, 1, 2, 19, 102, 377, 1104, 2777, 6282, 13155, 25998, 49153, 89792, 159681, 278034, 476131, 804790, 1346457, 2234768, 3686201, 6051290, 9897491, 16143262, 26275009, 42698112, 69304897, 112393634, 182155507, 295080582, 477850745 (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^4, 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..29.

Index entries for linear recurrences with constant coefficients, signature (6,-14,15,-5,-4,4,-1).

FORMULA

a(n)=6*a(n-1)-14*a(n-2)+15*a(n-3)-5*a(n-4)-4*a(n-5)+4*a(n-6)-a(n-7).

G.f.: -x*(-1+4*x-21*x^2-x^3-6*x^4+x^5) / ( (x^2+x-1)*(x-1)^5 ). - R. J. Mathar, May 12 2014

MATHEMATICA

(See A193046.)

CROSSREFS

Cf. A192232, A192744, A192951, A193046.

Sequence in context: A034572 A041393 A107123 * A055875 A089659 A240124

Adjacent sequences:  A193044 A193045 A193046 * A193048 A193049 A193050

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jul 15 2011

STATUS

approved

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Last modified October 17 16:06 EDT 2021. Contains 348065 sequences. (Running on oeis4.)