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

1,25

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.

Links

Table of n, a(n) for n=1..66.

Formula

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

Example

{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}

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}]

Crossrefs

Cf. A139147, A003269.

Sequence in context: A319582 A187447 A146292 * A279061 A206491 A359997

Adjacent sequences: A139036 A139037 A139038 * A139040 A139041 A139042

Keyword

nonn,tabl,uned

Author

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

Extensions

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

Status

approved