A176505 Triangle T(n,m) read by rows: T(n,m) = a(n) - a(m) - a(n-m) + 1, where a(n) = A000931(n+4).

1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 3, 2, 3, 2, 1, 1, 1, 2, 3, 4, 4, 4, 4, 3, 2, 1, 1, 2, 4, 5, 5, 6, 5, 5, 4, 2, 1

Offset: 0

Author

Roger L. Bagula, Apr 19 2010

Keywords

• nonn
• tabl
• easy
• less

Examples

			Triangle:
{1},
{1, 1},
{1, 0, 1},
{1, 0, 0, 1},
{1, 1, 1, 1, 1},
{1, 0, 1, 1, 0, 1},
{1, 1, 1, 2, 1, 1, 1},
{1, 1, 2, 2, 2, 2, 1, 1},
{1, 1, 2, 3, 2, 3, 2, 1, 1},
{1, 2, 3, 4, 4, 4, 4, 3, 2, 1},
{1, 2, 4, 5, 5, 6, 5, 5, 4, 2, 1},
...
T(6,3) = a(6) - a(3) - a(6-3) + 1 = a(6) - 2 * a(3) + 1 = 3 - (2 * 1) + 1 = 2. - _Indranil Ghosh_, Feb 17 2017
		

Links

• Indranil Ghosh, Rows 0..120, flattened
• Indranil Ghosh, Python Program to generate the b-file

Crossrefs

Cf. A000931.

Programs

Mathematica

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

Formula

T(n,m) = a(n) - a(m) - a(n-m) + 1, a(n) = A000931(n+4).

Extensions

Name and formula sections corrected by Indranil Ghosh, Feb 17 2017