|
%I #12 Dec 04 2016 19:46:25
%S 3,3,12,24,54,108,213,405,756,1386,2508,4488,7959,14007,24492,42588,
%T 73698,126996,218025,373065,636468,1082958,1838232,3113424,5262699,
%U 8879403,14956428,25153440,42241806,70844796
%N 0-sequence of reduction of (3n) by x^2 -> x+1.
%C See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]".
%F a(n) = 3*A190062(n).
%F G.f.: 3*x*(1-2*x+2*x^2)/(1-x)/(1-x-x^2)^2. [Colin Barker, Feb 11 2012]
%t c[n_] := 3 n; (* *)
%t Table[c[n], {n, 1, 15}]
%t q[x_] := x + 1;
%t p[0, x_] := 3; p[n_, x_] := p[n - 1, x] + (x^n)*c[n + 1]
%t reductionRules = {x^y_?EvenQ -> q[x]^(y/2),
%t x^y_?OddQ -> x q[x]^((y - 1)/2)};
%t t = Table[
%t Last[Most[
%t FixedPointList[Expand[#1 /. reductionRules] &, p[n, x]]]], {n, 0,
%t 30}]
%t Table[Coefficient[Part[t, n], x, 0], {n, 1, 30}] (* A192307 *)
%t Table[Coefficient[Part[t, n]/3, x, 0], {n, 1, 30}] (* A190062 *)
%t Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}] (* A192308 *)
%t Table[Coefficient[Part[t, n]/3, x, 1], {n, 1, 30}] (* A122491 *)
%t (* by _Peter J. C. Moses_, Jun 20 2011 *)
%Y Cf. A192232, A192307.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Jun 27 2011
|
