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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 (list; graph; refs; listen; history; text; internal format)
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*(1-4*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

Cf. A192232, A192247.

Sequence in context: A027847 A068841 A316982 * A124296 A223388 A152220

Adjacent sequences:  A192243 A192244 A192245 * A192247 A192248 A192249

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jun 27 2011

STATUS

approved

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Last modified April 7 10:56 EDT 2020. Contains 333301 sequences. (Running on oeis4.)