A129705 Triangle T(n,m) = A000071(n+2)-m*(m+1)/2 read by rows.

0, 1, 0, 2, 1, -1, 4, 3, 1, -2, 7, 6, 4, 1, -3, 12, 11, 9, 6, 2, -3, 20, 19, 17, 14, 10, 5, -1, 33, 32, 30, 27, 23, 18, 12, 5, 54, 53, 51, 48, 44, 39, 33, 26, 18, 88, 87, 85, 82, 78, 73, 67, 60, 52, 43, 143, 142, 140, 137, 133, 128, 122, 115, 107, 98, 88

Offset: 0

Author

Roger L. Bagula, Jun 08 2007

Keywords

• tabl
• easy
• sign

Comments

The row sums are 0, 1, 2, 6, 15, 37, 84, 180, 366, 715, 1353, 2498, 4524 = (n+1)*(A000071(n+2) -(n+2)*n/6). - R. J. Mathar, Sep 09 2011

Examples

			0;
1, 0;
2, 1, -1;
4, 3, 1, -2;
7, 6, 4, 1, -3;
12, 11, 9, 6, 2, -3;
20, 19, 17, 14, 10, 5, -1;
33, 32, 30, 27, 23, 18, 12, 5;
		

Links

• Eric Weisstein's World of Mathematics, Schubert Variety

Crossrefs

Cf. A000045.

Programs

Maple

A000071 := proc(n) if n = 0 then 0; else combinat[fibonacci](n)-1 ; end if; end proc:
A129705 := proc(n,m) A000071(n+2)-m*(m+1)/2 ; end proc: # R. J. Mathar, Sep 09 2011

Mathematica

fib[n_Integer?Positive] := fib[n] = fib[n - 1] + fib[n - 2]; fib[0] = 0; fib[1] = fib[2] = 1; t[n_, m_] = Sum[fib[i], {i, 0, n}] - Sum[i, {i, 0, m}]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]

Formula

t(n,m) = sum_{i=0..n} A000045(i) - sum_{i=0..m} i, 0<=m<=n.