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.

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

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 A343783 A261902

Adjacent sequences: A130751 A130752 A130753 * A130755 A130756 A130757

Keyword

nonn,tabf

Author

Roger L. Bagula, Jul 13 2007

Status

approved