%I
%S 1,1,8,21,63,156,371,827,1776,3687,7461,14776,28749,55101,104264,
%T 195121,361651,664660,1212431,2196935,3957136,7089331,12638953,
%U 22433136,39655993,69841561,122584136,214478637,374166471,650979852
%N 0sequence of reduction of (n^2+n+1) by x^2 > x+1.
%C See A192232 for definition of "ksequence of reduction of [sequence] by [substitution]".
%F Empirical G.f.: x*(13*x+7*x^23*x^3+3*x^4x^5)/(1x)/(1xx^2)^3. [Colin Barker, Feb 10 2012]
%t c[n_] := n^2 + n + 1;(* central polygonal numbers starting at 3 *)
%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]
%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}] (* A192300 *)
%t Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}] (* A192142 *)
%t (* by _Peter J. C. Moses_, Jun 20 2011 *)
%Y Cf. A192232, A192142.
%K nonn
%O 1,3
%A _Clark Kimberling_, Jun 27 2011
