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A192246
0-sequence of reduction of tetrahedral number sequence by x^2 -> x+1.
2
1, 1, 11, 31, 101, 269, 689, 1649, 3794, 8414, 18138, 38158, 78653, 159293, 317733, 625365, 1216455, 2341635, 4465645, 8445005, 15849556, 29541916, 54717716, 100766316, 184588041, 336489609, 610630959, 1103486539, 1986385449, 3562728009
OFFSET
1,3
COMMENTS
See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]".
FORMULA
Empirical G.f.: x*(1-4*x+12*x^2-12*x^3+5*x^4)/(1-x)/(1-x-x^2)^4. [Colin Barker, Feb 10 2012]
MATHEMATICA
c[n_] := n (n + 1) (n + 2)/6; (* tetrahedral numbers, A000292 *)
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}] (* A192246 *)
Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}] (* A192247 *)
(* by Peter J. C. Moses, Jun 26 2011 *)
CROSSREFS
Sequence in context: A027847 A068841 A316982 * A124296 A223388 A152220
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jun 27 2011
STATUS
approved