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 A192240 Constant term in the reduction of the polynomial (x+3)^n by x^2 -> x+1. 2
 1, 3, 10, 37, 149, 636, 2813, 12695, 57922, 265809, 1223521, 5640748, 26026505, 120137307, 554669594, 2561176781, 11826871933, 54615158940, 252210521317, 1164706900879, 5378632571666, 24838652091993, 114705606355625, 529714071477452 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A192232. LINKS FORMULA Empirical G.f. and recurrence: x*(1-4*x)/(1-7*x+11*x^2). a(n)=7*a(n-1)-11*a(n-2). [Colin Barker, Feb 09 2012] MATHEMATICA q[x_] := x + 1; p[n_, x_] := (x + 3)^n; reductionRules = {x^y_?EvenQ -> q[x]^(y/2),    x^y_?OddQ -> x q[x]^((y - 1)/2)}; t = Table[    Last[Most[      FixedPointList[Expand[#1 /. reductionRules] &, p[n, x]]]], {n, 0,      30}]; Table[Coefficient[Part[t, n], x, 0], {n, 1, 30}]  (* A192240 *) Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}]  (* A099453 *) (* by Peter J. C. Moses, Jun 26 2011 *) CROSSREFS Cf. A192232. Sequence in context: A199874 A151058 A044048 * A231894 A086444 A064613 Adjacent sequences:  A192237 A192238 A192239 * A192241 A192242 A192243 KEYWORD nonn AUTHOR Clark Kimberling, Jun 26 2011 STATUS approved

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Last modified February 19 19:30 EST 2020. Contains 332047 sequences. (Running on oeis4.)