

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
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OFFSET

0,3


COMMENTS

The titular polynomials are defined recursively: p(n,x)= x*p(n1,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(n1)  5*a(n2) + a(n3) + 2*a(n4)  a(n5).
G.f.: x*(1+3*x^2) / ( (x^2+x1)*(x1)^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



