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A192974 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments. 2
0, 1, 4, 14, 37, 84, 172, 329, 600, 1058, 1821, 3080, 5144, 8513, 13996, 22902, 37349, 60764, 98692, 160105, 259520, 420426, 680829, 1102224, 1784112, 2887489, 4672852, 7561694, 12236005, 19799268, 32036956, 51838025, 83876904, 135716978 (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) + 1 + 2*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..33.

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+3*x^2) / ( (x^2+x-1)*(x-1)^3 ). - R. J. Mathar, May 11 2014

MATHEMATICA

(See A192973.)

CROSSREFS

Cf. A192232, A192744, A192951, A192971.

Sequence in context: A027166 A126943 A209399 * A187428 A036368 A006071

Adjacent sequences:  A192971 A192972 A192973 * A192975 A192976 A192977

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jul 13 2011

STATUS

approved

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Last modified December 5 15:57 EST 2016. Contains 278770 sequences.