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Search: id:A157343
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| A157343 |
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A triangle sequence of polynomial coefficients: p(x,n)=If[PrimeQ[n], Sum[x^i, {i, 0, n}], (x + 1)*p(x, n - 1)]. |
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+0
1
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| 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 3, 4, 4, 4, 4, 4, 4, 3, 1, 1, 4, 7, 8, 8, 8, 8, 8, 7, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
(list; table; graph; listen)
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OFFSET
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0,12
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COMMENT
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Row sums are:
{1, 2, 3, 4, 8, 6, 12, 8, 16, 32, 64, 12, 24, 14, 28, 56}
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FORMULA
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p(x,n)=If[PrimeQ[n], Sum[x^i, {i, 0, n}], (x + 1)*p(x, n - 1)].
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EXAMPLE
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{1},
{1, 1},
{1, 1, 1},
{1, 1, 1, 1},
{1, 2, 2, 2, 1},
{1, 1, 1, 1, 1, 1},
{1, 2, 2, 2, 2, 2, 1},
{1, 1, 1, 1, 1, 1, 1, 1},
{1, 2, 2, 2, 2, 2, 2, 2, 1},
{1, 3, 4, 4, 4, 4, 4, 4, 3, 1},
{1, 4, 7, 8, 8, 8, 8, 8, 7, 4, 1},
{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1},
{1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1},
{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1},
{1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1},
{1, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 1}
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MATHEMATICA
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Clear[p, x, n, a];
p[x, 0] = 1; p[x, 1] = ((x + 1)); p[x, 2] = ((x^2 + x + 1));
p[x_, n_] := p[x, n] = If[PrimeQ[n], Sum[x^i, {i, 0, n}], (x + 1)*p[x, n - 1]];
a = Table[CoefficientList[FullSimplify[p[x, n]], x], {n, 0, 15}];
Flatten[a]
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CROSSREFS
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Sequence in context: A032548 A030597 A030599 this_sequence A102679 A025146 A067397
Adjacent sequences: A157340 A157341 A157342 this_sequence A157344 A157345 A157346
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 27 2009
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