# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a192248 Showing 1-1 of 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 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE