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A192247 1-sequence of reduction of tetrahedral number sequence by x^2 -> x+1. 2

%I #8 Dec 04 2016 19:46:25

%S 0,4,14,54,159,439,1111,2671,6136,13616,29346,61742,127262,257742,

%T 514102,1011862,1968265,3788845,7225565,13664305,25645120,47799824,

%U 88535124,163043324,298669724,544451624,988021646,1785478726,3214039171

%N 1-sequence of reduction of tetrahedral number sequence by x^2 -> x+1.

%C See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]".

%F Empirical G.f.: x^2*(2-x)*(2-2*x+3*x^2)/(1-x)/(1-x-x^2)^4. [Colin Barker, Feb 11 2012]

%t c[n_] := n (n + 1) (n + 2)/6; (* tetrahedral numbers, A000292 *)

%t Table[c[n], {n, 1, 15}]

%t q[x_] := x + 1;

%t p[0, x_] := 1; p[n_, x_] := p[n - 1, x] + (x^n)*c[n + 1]

%t reductionRules = {x^y_?EvenQ -> q[x]^(y/2),

%t x^y_?OddQ -> x q[x]^((y - 1)/2)};

%t t = Table[

%t Last[Most[

%t FixedPointList[Expand[#1 /. reductionRules] &, p[n, x]]]], {n, 0,

%t 30}]

%t Table[Coefficient[Part[t, n], x, 0], {n, 1, 30}] (* A192246 *)

%t Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}] (* A192247 *)

%t (* by _Peter J. C. Moses_, Jun 26 2011 *)

%Y Cf. A192232, A192246.

%K nonn

%O 1,2

%A _Clark Kimberling_, Jun 27 2011

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Last modified April 19 21:09 EDT 2024. Contains 371798 sequences. (Running on oeis4.)