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 A192469 Coefficient of x in the reduction by x^2->x+3 of the polynomial p(n,x)=1+x^n+x^(2n). 3
 2, 8, 44, 224, 1178, 6200, 32786, 173600, 919988, 4877072, 25858754, 137115440, 727074530, 3855471416, 20444603516, 108412922240, 574888887530, 3048505597160, 16165538467442, 85722217226576, 454565670533252, 2410459729834544 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For an introduction to reductions of polynomials by substitutions such as x^2->x+3, see A192232. LINKS FORMULA Empirical G.f.: -2*x*(x-1)*(3*x-1)/((3*x^2+x-1)*(9*x^2-7*x+1)). [Colin Barker, Nov 12 2012] EXAMPLE The first four polynomials p(n,x) and their reductions are as follows: p(1,x)=1+x+x^2 -> 4+2x p(2,x)=1+x^2+x^4 -> 16+8x p(3,x)=1+x^3+x^6 -> 61+44x p(4,x)=1+x^4+x^8 -> 304+224x. From these, read A192468=(4,16,61,304,...) and A192469=(2,8,44,224,...) MATHEMATICA (See A192468.) CROSSREFS Cf. A192232, A192468. Sequence in context: A264565 A018985 A018986 * A128656 A208044 A291697 Adjacent sequences: A192466 A192467 A192468 * A192470 A192471 A192472 KEYWORD nonn AUTHOR Clark Kimberling, Jul 01 2011 STATUS approved

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Last modified March 20 14:25 EDT 2023. Contains 361384 sequences. (Running on oeis4.)