Original entry on oeis.org
0, 1, 4, 18, 60, 186, 522, 1380, 3459, 8321, 19332, 43629, 96045, 206953, 437677, 910549, 1866952, 3778561, 7558953, 14963504, 29340482, 57033862, 109989752, 210575822, 400452782, 756836537, 1422191570, 2658250044, 4943946756, 9152396892
Offset: 1
A192248
0-sequence of reduction of binomial coefficient sequence B(n,4)=A000332 by x^2 -> x+1.
Original entry on oeis.org
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
Offset: 1
-
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 J. C. Moses, Jun 20 2011 *)
Showing 1-2 of 2 results.
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