A139039 A triangular central symmetric sequence based on the sequence A003269: if m <= floor(n/2), t(n,m) = A003269(m+2), otherwise t(n,m) = A003269(n - (m+2)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 3, 2, 1, 1, 1, 1, 1, 1, 2, 3, 3, 2, 1, 1, 1, 1, 1, 1, 2, 3, 4, 3, 2, 1, 1, 1

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, May 31 2008

Keywords

• nonn
• tabl
• uned

Comments

Row sums: {1, 2, 3, 4, 5, 6, 8, 10, 13, 16, 20, ...}. [Is this A186445 or A080078? - N. J. A. Sloane, Feb 10 2013]

The A003269 sequence is pushed back twice, so that the triangle is not almost all ones.

Examples

			{1},
{1, 1},
{1, 1, 1},
{1, 1, 1, 1},
{1, 1, 1, 1, 1},
{1, 1, 1, 1, 1, 1},
{1, 1, 1, 2, 1, 1, 1},
{1, 1, 1, 2, 2, 1, 1, 1},
{1, 1, 1, 2, 3, 2, 1, 1, 1},
{1, 1, 1, 2, 3, 3, 2, 1, 1, 1},
{1, 1, 1, 2, 3, 4, 3, 2, 1, 1, 1}
		

Crossrefs

Cf. A139147, A003269.

Programs

Mathematica

Clear[a]; a[ -2] = 0; a[ -1] = 1; a[0] = 1; a[1] = 1; a[n_] := a[n] = a[n - 1] + a[n - 4]; (* A003269 *) Table[If[m <= Floor[n/2],a[m],a[n-m] ] ,{n,0,10},{m,0,n}]

Formula

a(n) = a(n-1) + a(n-4); t(n,m) = a(m) if m <= floor(n/2), a(n-m) otherwise.

Extensions

Non-ASCII characters removed and Mathematica code corrected by Wouter Meeussen, Feb 10 2013