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A192244
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0-sequence of reduction of triangular number sequence by x^2 -> x+1.
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3
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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
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OFFSET
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1,3
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COMMENTS
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See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]".
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LINKS
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FORMULA
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Empirical G.f.: x*(1-3*x+6*x^2-3*x^3)/(1-x)/(1-x-x^2)^3. [Colin Barker, Feb 10 2012]
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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