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 A193007 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments. 1
 0, 1, 1, 9, 36, 108, 268, 591, 1201, 2303, 4232, 7534, 13096, 22357, 37649, 62749, 103772, 170616, 279300, 455747, 741905, 1205651, 1956816, 3173114, 5142096, 8329033, 13486753, 21833361, 35339796, 57195108, 92559292, 149781399, 242370481 (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)-1+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*(2*x^4-6*x^3+13*x^2-4*x+1)/((x-1)^4*(x^2+x-1)). [Colin Barker, Nov 12 2012] MATHEMATICA (See A193006.) CROSSREFS Cf. A192232, A192744, A192951, A193006. Sequence in context: A103158 A298442 A212104 * A259279 A168569 A213283 Adjacent sequences:  A193004 A193005 A193006 * A193008 A193009 A193010 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jul 14 2011 STATUS approved

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Last modified June 1 04:57 EDT 2020. Contains 334758 sequences. (Running on oeis4.)