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A192248 0-sequence of reduction of binomial coefficient sequence B(n,4)=A000332 by x^2 -> x+1.

%I A192248 #7 Dec 04 2016 19:46:25
%S A192248 1,1,16,51,191,569,1619,4259,10694,25709,59743,134818,296798,639518,
%T A192248 1352498,2813750,5769200,11676395,23358450,46239770,90667076,
%U A192248 176244326,339887026,650715076,1237467151,2338753519,4394813644,8214444389
%N A192248 0-sequence of reduction of binomial coefficient sequence B(n,4)=A000332 by x^2 -> x+1.
%C A192248 See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]".
%F A192248 Conjecture: G.f.: -x*(-1+5*x-20*x^2+30*x^3-25*x^4+8*x^5) / ( (x-1)*(x^2+x-1)^5 ). - _R. J. Mathar_, May 04 2014
%t A192248 c[n_] :=  n (n + 1) (n + 2) (n + 3)/24;  (* binomial B(n,4), A000332 *)
%t A192248 Table[c[n], {n, 1, 15}]
%t A192248 q[x_] := x + 1;
%t A192248 p[0, x_] := 1; p[n_, x_] := p[n - 1, x] + (x^n)*c[n + 1]
%t A192248 reductionRules = {x^y_?EvenQ -> q[x]^(y/2),
%t A192248    x^y_?OddQ -> x q[x]^((y - 1)/2)};
%t A192248 t = Table[
%t A192248   Last[Most[
%t A192248     FixedPointList[Expand[#1 /. reductionRules] &, p[n, x]]]], {n, 0,
%t A192248    40}]
%t A192248 Table[Coefficient[Part[t, n], x, 0], {n, 1, 40}]  (* A192248 *)
%t A192248 Table[Coefficient[Part[t, n], x, 1], {n, 1, 40}]  (* A192249 *)
%t A192248 Table[Coefficient[Part[t, n]/5, x, 1], {n, 1, 40}]  (* A192069 *)
%t A192248 (* by _Peter J. C. Moses_, Jun 20 2011 *)
%Y A192248 Cf. A192232, A192249, A192069.
%K A192248 nonn
%O A192248 1,3
%A A192248 _Clark Kimberling_, Jun 27 2011