A139038 Centrally symmetric triangle read by rows: t(n,m) = A000931(m+1) if m <= floor(n/2), A000931(n - m+1) otherwise.

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

Offset

1,13

Comments

Row sums: {1, 2, 3, 4, 6, 8, 10, 12, 15, 18, 22, ...}.

The Padovan sequence is pushed back to a(-1)=1, so that the triangle is not almost all ones.

Links

Table of n, a(n) for n=1..65.

Formula

a(n) = a(n-2) + a(n-3);

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

Mathematica

Clear[a] a[ -1] = 1; a[0] = 1; a[1] = 1; a[n_] := a[n] = a[n - 2] + a[n - 3]; (* Padovan : A000931 *) Table[If[m <= Floor[n/2], a[m], a[n - m]], {n, 0, 10}, {m, 0, n}]
(* Alternative Mathematica function*) t[n_, m_] = Min[1 + Floor[m/2], 1 + Floor[(n - m)/2]]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]

Crossrefs

Cf. A139147.

Sequence in context: A155052 A096284 A163100 * A322812 A259094 A306741

Adjacent sequences: A139035 A139036 A139037 * A139039 A139040 A139041

Keyword

nonn,tabl

Author

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

Extensions

Edited by N. J. A. Sloane, Feb 28 2009

Non-ASCII characters in %t line corrected by Wouter Meeussen, Feb 10 2013

Status

approved