A192311 0-sequence of reduction of (3n-2) by x^2 -> x+1.

1, 1, 8, 18, 44, 92, 187, 363, 688, 1276, 2330, 4200, 7493, 13253, 23272, 40614, 70504, 121828, 209663, 359535, 614576, 1047536, 1780918, 3020688, 5112649, 8636617, 14563592, 24517818, 41213348, 69180716, 115975555, 194187315, 324775408, 542606308, 905637842

Offset

1,3

Comments

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

Links

Table of n, a(n) for n=1..35.

Formula

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

Mathematica

c[n_] := 3 n - 2;
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}]  (* A192311 *)
Table[Coefficient[Part[t, n], x, 1], {n, 1, 40}]  (* A192312 *)
(* Peter J. C. Moses, Jun 20 2011 *)

Crossrefs

Cf. A192232, A192312.

Sequence in context: A211527 A279899 A395591 * A300161 A034714 A153388

Adjacent sequences: A192308 A192309 A192310 * A192312 A192313 A192314

Keyword

nonn

Author

Clark Kimberling, Jun 27 2011

Extensions

More terms from Jason Yuen, Aug 23 2025

Status

approved