A176700 Triangle T(n,m) = 2+A176697(n)-A176697(m)-A176697(n-m) read along rows 0<=m<=n.

1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 14, 16, 14, 1, 1, 44, 55, 55, 44, 1, 1, 146, 187, 196, 187, 146, 1, 1, 504, 647, 686, 686, 647, 504, 1, 1, 1786, 2287, 2428, 2458, 2428, 2287, 1786, 1, 1, 6449, 8232, 8731, 8863, 8863, 8731, 8232, 6449, 1, 1, 23635, 30081, 31862, 32352

Offset: 0

Author

Roger L. Bagula, Apr 24 2010

Keywords

• nonn
• tabl
• easy

Comments

Row sums are 1, 2, 5, 12, 46, 200, 864, 3676, 15462, 64552, 268316,...

Examples

			1;
1, 1;
1, 3, 1;
1, 5, 5, 1;
1, 14, 16, 14, 1;
1, 44, 55, 55, 44, 1;
1, 146, 187, 196, 187, 146, 1;
1, 504, 647, 686, 686, 647, 504, 1;
1, 1786, 2287, 2428, 2458, 2428, 2287, 1786, 1;
1, 6449, 8232, 8731, 8863, 8863, 8731, 8232, 6449, 1;
1, 23635, 30081, 31862, 32352, 32454, 32352, 31862, 30081, 23635, 1;
		

Crossrefs

Cf. A176697.

Programs

Maple

A176700 :=proc(n,k)
    2+A176697(n)-A176697(k)-A176697(n-k) ;
end proc: # R. J. Mathar, Jun 17 2015

Mathematica

a[0] := 1; a[1] := 1;a[2]=3
a[n_] := a[n] = Table[a[i], {i, 0, n - 1}].Table[a[n - 1 - i], {i, 0, n - 1}];
t[n_, m_] := 2 + (-a[m] - a[n - m] + a[n]);
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]

Formula

T(n,k) = T(n,n-k).