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 A192307 0-sequence of reduction of (3n) by x^2 -> x+1. 2
 3, 3, 12, 24, 54, 108, 213, 405, 756, 1386, 2508, 4488, 7959, 14007, 24492, 42588, 73698, 126996, 218025, 373065, 636468, 1082958, 1838232, 3113424, 5262699, 8879403, 14956428, 25153440, 42241806, 70844796 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]". LINKS FORMULA a(n) = 3*A190062(n). G.f.: 3*x*(1-2*x+2*x^2)/(1-x)/(1-x-x^2)^2. [Colin Barker, Feb 11 2012] MATHEMATICA c[n_] := 3 n; (*  *) Table[c[n], {n, 1, 15}] q[x_] := x + 1; p[0, x_] := 3; p[n_, x_] := p[n - 1, x] + (x^n)*c[n + 1] 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}]  (* A192307 *) Table[Coefficient[Part[t, n]/3, x, 0], {n, 1, 30}]  (* A190062 *) Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}]  (* A192308 *) Table[Coefficient[Part[t, n]/3, x, 1], {n, 1, 30}]  (* A122491 *) (* by Peter J. C. Moses, Jun 20 2011 *) CROSSREFS Cf. A192232, A192307. Sequence in context: A268798 A136533 A268639 * A328150 A161804 A097342 Adjacent sequences:  A192304 A192305 A192306 * A192308 A192309 A192310 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jun 27 2011 STATUS approved

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Last modified July 28 23:26 EDT 2021. Contains 346340 sequences. (Running on oeis4.)