

A192244


0sequence of reduction of triangular number sequence by x^2 > x+1.


3



1, 1, 7, 17, 47, 110, 250, 538, 1123, 2278, 4522, 8812, 16911, 32031, 59991, 111263, 204593, 373370, 676800, 1219440, 2185251, 3896796, 6917892, 12231192, 21544717, 37819885, 66179335, 115464893, 200906723, 348688838
(list;
graph;
refs;
listen;
history;
text;
internal format)



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+6*x^23*x^3)/(1x)/(1xx^2)^3. [Colin Barker, Feb 10 2012]


MATHEMATICA

c[n_] := n (n + 1)/2; (* triangular numbers, A000217 *)
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]
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}] (* A192244 *)
Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}] (* A192245 *)
(* by Peter J. C. Moses, Jun 26 2011 *)


CROSSREFS

Cf. A192232, A192245.
Sequence in context: A061722 A195905 A104164 * A110097 A179262 A018672
Adjacent sequences: A192241 A192242 A192243 * A192245 A192246 A192247


KEYWORD

nonn


AUTHOR

Clark Kimberling, Jun 26 2011


STATUS

approved



