

A192143


0sequence of reduction of hexagonal numbers sequence by x^2 > x+1.


2



1, 1, 16, 44, 134, 332, 787, 1747, 3736, 7726, 15580, 30760, 59685, 114117, 215472, 402464, 744674, 1366484, 2489175, 4504695, 8104536, 14504226, 25833336, 45811344, 80916169, 142400137, 249760912, 436706132, 761385086, 1323910556
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OFFSET

1,3


COMMENTS

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


LINKS

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


FORMULA

Empirical G.f.: x*(13*x+15*x^212*x^3+6*x^4)/(1x)/(1xx^2)^3. [Colin Barker, Feb 11 2012]


MATHEMATICA

c[n_] := n (2 n  1); (* hexagonal numbers, A000384 *)
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}] (* A192143 *)
Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}] (* A192144 *)
(* by Peter J. C. Moses, Jun 20 2011 *)


CROSSREFS

Cf. A192232, A192144.
Sequence in context: A211573 A211582 A204032 * A221593 A300962 A051868
Adjacent sequences: A192140 A192141 A192142 * A192144 A192145 A192146


KEYWORD

nonn


AUTHOR

Clark Kimberling, Jun 27 2011


STATUS

approved



