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A193045 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments. 1
0, 1, 1, 3, 8, 21, 49, 105, 210, 399, 729, 1293, 2242, 3821, 6427, 10703, 17690, 29073, 47579, 77621, 126340, 205291, 333171, 540233, 875428, 1417961, 2295989, 3716875, 6016140, 9736669, 15756869, 25498033, 41259862, 66763351, 108029197 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The titular polynomials are defined recursively:  p(n,x)=x*p(n-1,x)+n(-1+n^2)/6, 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 (5,-9,6,1,-3,1)

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*(1-4*x+7*x^2-4*x^3+x^4) / ( (x^2+x-1)*(x-1)^4 ). - R. J. Mathar, May 12 2014

MATHEMATICA

(See A193044.)

CROSSREFS

Cf. A192232, A192744, A192951, A193044.

Sequence in context: A007773 A071078 A179903 * A238831 A322059 A259714

Adjacent sequences:  A193042 A193043 A193044 * A193046 A193047 A193048

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jul 15 2011

STATUS

approved

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Last modified September 20 08:13 EDT 2019. Contains 327214 sequences. (Running on oeis4.)