Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
(* by _Peter J. C. Moses, _, Jun 20 2011 *)
editing
approved
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
approved
editing
_Clark Kimberling (ck6(AT)evansville.edu), _, Jun 27 2011
proposed
approved
allocated for Clark Kimberling0-sequence of reduction of binomial coefficient sequence B(n,4)=A000332 by x^2 -> x+1.
1, 1, 16, 51, 191, 569, 1619, 4259, 10694, 25709, 59743, 134818, 296798, 639518, 1352498, 2813750, 5769200, 11676395, 23358450, 46239770, 90667076, 176244326, 339887026, 650715076, 1237467151, 2338753519, 4394813644, 8214444389
1,3
See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]".
c[n_] := n (n + 1) (n + 2) (n + 3)/24; (* binomial B(n, 4), A000332 *)
Table[c[n], {n, 1, 15}]
q[x_] := x + 1;
p[0, x_] := 1; p[n_, x_] := p[n - 1, x] + (x^n)*c[n + 1]
reductionRules = {x^y_?EvenQ -> q[x]^(y/2),
x^y_?OddQ -> x q[x]^((y - 1)/2)};
t = Table[
Last[Most[
FixedPointList[Expand[#1 /. reductionRules] &, p[n, x]]]], {n, 0,
40}]
Table[Coefficient[Part[t, n], x, 0], {n, 1, 40}] (* A192248 *)
Table[Coefficient[Part[t, n], x, 1], {n, 1, 40}] (* A192249 *)
Table[Coefficient[Part[t, n]/5, x, 1], {n, 1, 40}] (* A192069 *)
(* by Peter Moses, Jun 20 2011 *)
allocated
nonn
Clark Kimberling (ck6(AT)evansville.edu), Jun 27 2011
approved
proposed
allocated for Clark Kimberling
allocated
approved