A139038 Triangle read by rows: T(n,m) = A000931(m+6) if m <= floor(n/2), A000931(n+6-m) otherwise, for 0 <= m <= n.

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

0,13

Comments

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=0..64.

Example

The triangle begins:
  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

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}]

Crossrefs

Cf. A000931, A139147.

Sequence in context: A155052 A096284 A163100 * A322812 A259094 A306741

Adjacent sequences: A139035 A139036 A139037 * A139039 A139040 A139041

Keyword

nonn,tabl,less

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

Definition corrected and offset changed by Georg Fischer, May 16 2024

Status

approved