A173389 A shifted symmetrical triangular sequence:t(n,m)=If[Mod[n, 2] == 0, Binomial[n, m], Binomial[n - 1, m - 1] + If[(n - 3)*(m - 2) >= 1, Binomial[n - 3, m - 2], 0]]

1, 0, 1, 1, 2, 1, 0, 1, 2, 1, 1, 4, 6, 4, 1, 0, 1, 4, 8, 5, 1, 1, 6, 15, 20, 15, 6, 1, 0, 1, 6, 19, 26, 19, 7, 1, 1, 8, 28, 56, 70, 56, 28, 8, 1, 0, 1, 8, 34, 71, 90, 71, 34, 9, 1, 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1

Offset

0,5

Comments

Row sums are: {1, 1, 4, 4, 16, 19, 64, 79, 256, 319, 1024,...}.

The sequence is designed to be symmetrical with every other row shifted to the right and a symmetrical term added to is so that the row sums aren't the same.

Links

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

Formula

t(n,m)=If[Mod[n, 2] == 0, Binomial[n, m], Binomial[n - 1, m - 1] + If[(n - 3)*(m - 2) >= 1, Binomial[n - 3, m - 2], 0]]

Example

{1},
{0, 1},
{1, 2, 1},
{0, 1, 2, 1},
{1, 4, 6, 4, 1},
{0, 1, 4, 8, 5, 1},
{1, 6, 15, 20, 15, 6, 1},
{0, 1, 6, 19, 26, 19, 7, 1},
{1, 8, 28, 56, 70, 56, 28, 8, 1},
{0, 1, 8, 34, 71, 90, 71, 34, 9, 1},
{1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1}

Mathematica

t[n_, m_] = If[Mod[n, 2] == 0, Binomial[n, m], Binomial[n - 1, m - 1] + If[(n - 3)*(m - 2) >= 1, Binomial[n - 3, m - 2], 0]];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A366951 A029359 A349815 * A241062 A333471 A360711

Adjacent sequences: A173386 A173387 A173388 * A173390 A173391 A173392

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Feb 17 2010

Status

approved