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 A193005 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments. 1
 0, 1, 2, 11, 40, 115, 280, 611, 1234, 2357, 4320, 7677, 13328, 22733, 38258, 63735, 105368, 173199, 283480, 462511, 752850, 1223361, 1985472, 3219481, 5217120, 8450425, 13683170, 22151171, 35854024, 58027147, 93905560, 151959707, 245895058, 397887533 (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^3, 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 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*(1-3*x+10*x^2-3*x^3+x^4) / ( (x^2+x-1)*(x-1)^4 ). - R. J. Mathar, May 12 2014 a(n) = 10*F(n+4) + 4*F(n+5) - 50 - 24*n - 6*n^2 - n^3, where F = A000045. - Greg Dresden, Jan 01 2021 MATHEMATICA (See A193004.) CROSSREFS Cf. A192232, A192744, A192951, A193004, A000045. Sequence in context: A125064 A274326 A055329 * A152895 A308524 A335629 Adjacent sequences:  A193002 A193003 A193004 * A193006 A193007 A193008 KEYWORD nonn AUTHOR Clark Kimberling, Jul 14 2011 STATUS approved

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Last modified May 12 04:27 EDT 2021. Contains 343810 sequences. (Running on oeis4.)