

A130754


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.


0



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
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OFFSET

1,2


COMMENTS

This fold back operation leaves the row sums at 2^n.


LINKS

Table of n, a(n) for n=1..66.


FORMULA

a(n,i)== If[n > 0 && i == 0, 2, If[Mod[n, 2] == 0, binomial[n, i], 2*binomial[n, i]]];


EXAMPLE

{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}


MATHEMATICA

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[%]


CROSSREFS

Cf. A007318.
Sequence in context: A156717 A198889 A329814 * A164126 A261902 A163368
Adjacent sequences: A130751 A130752 A130753 * A130755 A130756 A130757


KEYWORD

nonn,tabf


AUTHOR

Roger L. Bagula, Jul 13 2007


STATUS

approved



