A143087 Symmetrical triangle sequence: t(n,m)=If[m <= Floor[n/2], 2^(m + 1) - 1, 2^(n - m + 1) - 1]*Binomial[n, m].

1, 1, 1, 1, 6, 1, 1, 9, 9, 1, 1, 12, 42, 12, 1, 1, 15, 70, 70, 15, 1, 1, 18, 105, 300, 105, 18, 1, 1, 21, 147, 525, 525, 147, 21, 1, 1, 24, 196, 840, 2170, 840, 196, 24, 1, 1, 27, 252, 1260, 3906, 3906, 1260, 252, 27, 1, 1, 30, 315, 1800, 6510, 15876, 6510, 1800, 315, 30, 1

Offset

1,5

Comments

Row sums are:

{1, 2, 8, 20, 68, 172, 548, 1388, 4292, 10892, 33188}.

Links

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

Formula

t(n,m)=If[m <= Floor[n/2], 2^(m + 1) - 1, 2^(n - m + 1) - 1]*Binomial[n, m].

Example

{1},
{1, 1},
{1, 6, 1},
{1, 9, 9, 1},
{1, 12, 42, 12, 1},
{1, 15, 70, 70, 15, 1},
{1, 18, 105, 300, 105, 18, 1},
{1, 21, 147, 525, 525, 147, 21, 1},
{1, 24, 196, 840, 2170, 840, 196, 24, 1},
{1, 27, 252, 1260, 3906, 3906, 1260, 252, 27, 1},
{1, 30, 315, 1800, 6510, 15876, 6510, 1800, 315, 30, 1}

Mathematica

Table[Table[If[m <= Floor[n/2], 2^(m + 1) - 1, 2^(n - m + 1) - 1]*Binomial[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]

Crossrefs

Sequence in context: A189089 A132047 A140284 * A144470 A174377 A176151

Adjacent sequences: A143084 A143085 A143086 * A143088 A143089 A143090

Keyword

nonn,uned

Author

Roger L. Bagula and Gary W. Adamson, Oct 16 2008

Status

approved