A192309 0-sequence of reduction of (3n-1) by x^2 -> x+1.

2, 2, 10, 21, 49, 100, 200, 384, 722, 1331, 2419, 4344, 7726, 13630, 23882, 41601, 72101, 124412, 213844, 366300, 625522, 1065247, 1809575, 3067056, 5187674, 8758010, 14760010, 24835629, 41727577, 70012756

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..30.

Formula

Empirical G.f.: x*(2-4*x+6*x^2-x^3)/(1-3*x+x^2+3*x^3-x^4-x^5). [Colin Barker, Feb 09 2012]

Mathematica

c[n_] := 3 n - 1;
Table[c[n], {n, 1, 15}]
q[x_] := x + 1;
p[0, x_] := 2; 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}]  (* A192309 *)
Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}]  (* A192310 *)
(* by Peter J. C. Moses, Jun 20 2011 *)

Crossrefs

Cf. A192232, A192310.

Sequence in context: A303565 A291856 A358996 * A151456 A336490 A230893

Adjacent sequences: A192306 A192307 A192308 * A192310 A192311 A192312

Keyword

nonn

Author

Clark Kimberling, Jun 27 2011

Status

approved