A192143 - OEIS

A192143

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

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 "k-sequence of reduction of [sequence] by [substitution]".

LINKS

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

FORMULA

Empirical G.f.: x*(1-3*x+15*x^2-12*x^3+6*x^4)/(1-x)/(1-x-x^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 A359704

Adjacent sequences: A192140 A192141 A192142 * A192144 A192145 A192146

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jun 27 2011

STATUS

approved