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A171145
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The sequence of coefficients of a polynomial recursion: p(x,n)=If[Mod[n, 2] == 0, (x + 1)*p(x, n - 1), (x^2 + n*x + 1)^Floor[n/2]].
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0
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1, 1, 1, 1, 3, 1, 1, 4, 4, 1, 1, 10, 27, 10, 1, 1, 11, 37, 37, 11, 1, 1, 21, 150, 385, 150, 21, 1, 1, 22, 171, 535, 535, 171, 22, 1, 1, 36, 490, 3024, 7539, 3024, 490, 36, 1, 1, 37, 526, 3514, 10563, 10563, 3514, 526, 37, 1, 1, 55, 1215, 13530, 76845, 188001, 76845
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OFFSET
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1,5
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COMMENTS
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Row sums are:
{1, 2, 5, 10, 49, 98, 729, 1458, 14641, 29282, 371293, 742586,...}.
The modulo 2 of this appears to be a staggered Sierpinski-type fractal.
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LINKS
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FORMULA
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p(x,n)=If[Mod[n, 2] == 0, (x + 1)*p(x, n - 1), (x^2 + n*x + 1)^Floor[n/2]]
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EXAMPLE
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{1},
{1, 1},
{1, 3, 1},
{1, 4, 4, 1},
{1, 10, 27, 10, 1},
{1, 11, 37, 37, 11, 1},
{1, 21, 150, 385, 150, 21, 1},
{1, 22, 171, 535, 535, 171, 22, 1},
{1, 36, 490, 3024, 7539, 3024, 490, 36, 1},
{1, 37, 526, 3514, 10563, 10563, 3514, 526, 37, 1},
{1, 55, 1215, 13530, 76845, 188001, 76845, 13530, 1215, 55, 1},
{1, 56, 1270, 14745, 90375, 264846, 264846, 90375, 14745, 1270, 56, 1}
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MATHEMATICA
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Clear[p, n, x, a]
p[x, 1] := 1;
p[x_, n_] := p[x, n] = If[Mod[n, 2] == 0, (x + 1)*p[x, n - 1], (x^2 + n*x + 1)^Floor[n/2]];
a = Table[CoefficientList[p[x, n], x], {n, 1, 12}];
Flatten[a]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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