A157873 Triangle T(n,m)= binomial(n,2^m) + binomial(n,2^(n - m)) read by rows.

0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 6, 2, 6, 4, 5, 10, 5, 5, 10, 5, 6, 15, 15, 0, 15, 15, 6, 7, 21, 35, 0, 0, 35, 21, 7, 8, 28, 70, 1, 0, 1, 70, 28, 8, 9, 36, 126, 9, 0, 0, 9, 126, 36, 9, 10, 45, 210, 45, 0, 0, 0, 45, 210, 45, 10

Offset

0,4

Comments

Row sums are {0, 2, 6, 12, 22, 40, 72, 126, 214, 360, 620,...}.

Links

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

Formula

T(n,m)=binomial(n, 2^m) + binomial(n, 2^(n - m)) = T(n,n-m).

Example

{0},
{1, 1},
{2, 2, 2},
{3, 3, 3, 3},
{4, 6, 2, 6, 4},
{5, 10, 5, 5, 10, 5},
{6, 15, 15, 0, 15, 15, 6},
{7, 21, 35, 0, 0, 35, 21, 7},
{8, 28, 70, 1, 0, 1, 70, 28, 8},
{9, 36, 126, 9, 0, 0, 9, 126, 36, 9},
{10, 45, 210, 45, 0, 0, 0, 45, 210, 45, 10}

Mathematica

t[n_, m_] = Binomial[n, 2^m] + Binomial[n, 2^(n - m)];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A352100 A216200 A376696 * A022870 A237050 A235130

Adjacent sequences: A157870 A157871 A157872 * A157874 A157875 A157876

Keyword

nonn,tabl

Author

Roger L. Bagula, Mar 08 2009

Extensions

Edited by the Associate Editors of the OEIS, Apr 10 2009

Status

approved