A147289 A multi-shifted and scaled Pascal triangle: t(n,m)=Binomial[n, m] + Sum[If[n >= 2*k,2*Binomial[n - 2*k, m - k], 0], {k, 1, Floor[n/2]}].

1, 1, 1, 1, 4, 1, 1, 5, 5, 1, 1, 6, 12, 6, 1, 1, 7, 18, 18, 7, 1, 1, 8, 25, 38, 25, 8, 1, 1, 9, 33, 63, 63, 33, 9, 1, 1, 10, 42, 96, 128, 96, 42, 10, 1, 1, 11, 52, 138, 224, 224, 138, 52, 11, 1, 1, 12, 63, 190, 362, 450, 362, 190, 63, 12, 1

Offset

0,5

Comments

The row sums are: {1, 2, 6, 12, 26, 52, 106, 212, 426, 852, 1706, ...}.

Links

Table of n, a(n) for n=0..65.

Formula

t(n,m)=Binomial[n, m] + Sum[If[n >= 2*k,2*Binomial[n - 2*k, m - k], 0], {k, 1, Floor[n/2]}].

Example

{1}, {1, 1}, {1, 4, 1}, {1, 5, 5, 1}, {1, 6, 12, 6, 1}, {1, 7, 18, 18, 7, 1}, {1, 8, 25, 38, 25, 8, 1}, {1, 9, 33, 63, 63, 33, 9, 1}, {1, 10, 42, 96, 128, 96, 42, 10, 1}, {1, 11, 52, 138, 224, 224, 138, 52, 11, 1}, {1, 12, 63, 190, 362, 450, 362, 190, 63, 12, 1}

Mathematica

Table[Binomial[n, m] + Sum[If[n >= 2*k, 2*Binomial[n - 2*k, m - k], 0], {k, 1, Floor[n/2]}], {n, 0, 10}, {m, 0, n}]; Flatten[%]

Crossrefs

Sequence in context: A173740 A028275 A173118 * A147566 A204621 A146770

Adjacent sequences: A147286 A147287 A147288 * A147290 A147291 A147292

Keyword

nonn,tabl

Author

Roger L. Bagula, Nov 04 2008

Extensions

Edited by N. J. A. Sloane, Nov 07 2008

Status

approved