A176480 Triangle: let b(n) = 3*b(n - 1) - 2*b(n - 2) + b(n - 3), then T(n,m) = b(n) - b(m) - b(n - m) + 1.

1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 9, 11, 9, 1, 1, 21, 28, 28, 21, 1, 1, 49, 68, 73, 68, 49, 1, 1, 114, 161, 178, 178, 161, 114, 1, 1, 265, 377, 422, 434, 422, 377, 265, 1, 1, 616, 879, 989, 1029, 1029, 989, 879, 616, 1, 1, 1432, 2046, 2307, 2412, 2440, 2412, 2307, 2046

Offset

0,5

Links

Table of n, a(n) for n=0..63.

Example

{1},
{1, 1},
{1, 2, 1},
{1, 4, 4, 1},
{1, 9, 11, 9, 1},
{1, 21, 28, 28, 21, 1},
{1, 49, 68, 73, 68, 49, 1},
{1, 114, 161, 178, 178, 161, 114, 1},
{1, 265, 377, 422, 434, 422, 377, 265, 1},
{1, 616, 879, 989, 1029, 1029, 989, 879, 616, 1},
{1, 1432, 2046, 2307, 2412, 2440, 2412, 2307, 2046, 1432, 1}

Mathematica

b[0] := 0; b[1] := 1; b[2] := 3;
b[n_] := b[n] = 3*b[n - 1] - 2*b[n - 2] + b[n - 3];
t[n_, m_] := t[n, m] = b[n] - b[m] - b[n - m] + 1;
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Cf. A095263

Sequence in context: A268079 A202549 A155971 * A154218 A373744 A326326

Adjacent sequences: A176477 A176478 A176479 * A176481 A176482 A176483

Keyword

nonn,tabl,easy

Author

Roger L. Bagula, Apr 18 2010

Status

approved