A192247 1-sequence of reduction of tetrahedral number sequence by x^2 -> x+1.

0, 4, 14, 54, 159, 439, 1111, 2671, 6136, 13616, 29346, 61742, 127262, 257742, 514102, 1011862, 1968265, 3788845, 7225565, 13664305, 25645120, 47799824, 88535124, 163043324, 298669724, 544451624, 988021646, 1785478726, 3214039171

Offset

1,2

Comments

See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]".

Links

Table of n, a(n) for n=1..29.

Formula

Empirical G.f.: x^2*(2-x)*(2-2*x+3*x^2)/(1-x)/(1-x-x^2)^4. [Colin Barker, Feb 11 2012]

Mathematica

c[n_] := n (n + 1) (n + 2)/6;  (* tetrahedral numbers, A000292 *)
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,
   30}]
Table[Coefficient[Part[t, n], x, 0], {n, 1, 30}]  (* A192246 *)
Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}]  (* A192247 *)
(* by Peter J. C. Moses, Jun 26 2011 *)

Crossrefs

Cf. A192232, A192246.

Sequence in context: A162482 A308555 A000651 * A118896 A145211 A060898

Adjacent sequences: A192244 A192245 A192246 * A192248 A192249 A192250

Keyword

nonn

Author

Clark Kimberling, Jun 27 2011

Status

approved