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Search: id:A130754
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| A130754 |
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A folded back triangular sequence of the binomial / Pascal's triangle A007318: half of the sequence is taken and doubled except for the odd middle terms which remain the same. |
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+0
1
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| 1, 2, 2, 2, 2, 6, 2, 4, 6, 2, 10, 20, 2, 6, 15, 20, 2, 14, 42, 70, 2, 8, 28, 56, 70, 2, 18, 72, 168, 252, 2, 10, 45, 120, 210, 252, 2, 22, 110, 330, 660, 924, 2, 12, 66, 220, 495, 792, 924, 2, 26, 156, 572, 1430, 2574, 3432, 2, 14, 91, 364, 1001, 2002, 3003, 3432, 2, 30
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This fold back operation leaves the row sums at 2^n.
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FORMULA
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a(n,i)== If[n > 0 && i == 0, 2, If[Mod[n, 2] == 0, binomial[n, i], 2*binomial[n, i]]];
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EXAMPLE
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{1},
{2},
{2, 2},
{2, 6},
{2, 4, 6},
{2, 10, 20},
{2, 6, 15, 20},
{2, 14, 42, 70},
{2, 8, 28, 56, 70},
{2, 18, 72, 168, 252},
{2, 10, 45, 120, 210, 252}
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MATHEMATICA
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f[n_, i_] = If[n > 0 && i == 0, 2, If[Mod[n, 2] == 0, Binomial[n, i], 2*Binomial[n, i]]]; Table[Table[f[n, i], {i, 0, Floor[n/2]}], {n, 0, 20}]; Flatten[%]
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CROSSREFS
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Cf. A007318.
Sequence in context: A073124 A070877 A156717 this_sequence A164126 A163368 A151948
Adjacent sequences: A130751 A130752 A130753 this_sequence A130755 A130756 A130757
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KEYWORD
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nonn,tabf
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jul 13 2007
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