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%I #9 Dec 04 2016 19:46:25
%S 1,1,16,44,134,332,787,1747,3736,7726,15580,30760,59685,114117,215472,
%T 402464,744674,1366484,2489175,4504695,8104536,14504226,25833336,
%U 45811344,80916169,142400137,249760912,436706132,761385086,1323910556
%N 0-sequence of reduction of hexagonal numbers sequence by x^2 -> x+1.
%C See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]".
%F Empirical G.f.: x*(1-3*x+15*x^2-12*x^3+6*x^4)/(1-x)/(1-x-x^2)^3. [Colin Barker, Feb 11 2012]
%t c[n_] := n (2 n - 1); (* hexagonal numbers, A000384 *)
%t Table[c[n], {n, 1, 15}]
%t q[x_] := x + 1;
%t p[0, x_] := 1; 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}] (* A192143 *)
%t Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}] (* A192144 *)
%t (* by _Peter J. C. Moses_, Jun 20 2011 *)
%Y Cf. A192232, A192144.
%K nonn
%O 1,3
%A _Clark Kimberling_, Jun 27 2011
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