A131127 Table read by rows: 2*A007318(n,m) - A167374(n,m).

1, 3, 1, 2, 5, 1, 2, 6, 7, 1, 2, 8, 12, 9, 1, 2, 10, 20, 20, 11, 1, 2, 12, 30, 40, 30, 13, 1, 2, 14, 42, 70, 70, 42, 15, 1, 2, 16, 56, 112, 140, 112, 56, 17, 1, 2, 18, 72, 168, 252, 252, 168, 72, 19, 1, 2, 20, 90, 240, 420, 504, 420, 240, 90, 21, 1, 2, 22, 110, 330, 660, 924, 924, 660, 330, 110, 23, 1

Offset

0,2

Comments

Row sums = A000079(n+1), n>0.

Warning: row sums are not A046055! - N. J. A. Sloane, Jul 08 2009

Row sums = A151821(n+1), n>=0. - Alois P. Heinz, Jul 13 2009

A167374 is a modified version of the pair operator A097806 with (1,1,1,...) in the main diagonal and (-1,-1,-1,...) in the subdiagonal.

Links

Alois P. Heinz, Rows n = 0..140, flattened

Example

First few rows of the triangle:
  1;
  3,  1;
  2,  5,  1;
  2,  6,  7,  1;
  2,  8, 12,  9,  1;
  2, 10, 20, 20, 11,  1;
  ...

Maple

T:= (n, m)-> 2*binomial(n, m) -(-1)^(n+m)*`if`(n=m or n=m+1, 1, 0): seq(seq(T(n, m), m=0..n), n=0..12); # Alois P. Heinz, Jul 13 2009

Mathematica

T[n_, m_] := 2*Binomial[n, m] - (-1)^(n+m)*If[n == m || n == m+1, 1, 0];
Table[Table[T[n, m], {m, 0, n}], {n, 0, 12}] // Flatten (* Jean-François Alcover, May 19 2016, translated from Maple *)

Crossrefs

Cf. A007318, A097806, A151821, A167374.

Sequence in context: A211025 A125704 A357498 * A113141 A134225 A136081

Adjacent sequences: A131124 A131125 A131126 * A131128 A131129 A131130

Keyword

nonn,tabl

Author

Gary W. Adamson, Jun 16 2007

Extensions

Edited by N. J. A. Sloane and R. J. Mathar, Jul 09 2009

Corrected and extended by Alois P. Heinz, Jul 13 2009

Definition simplified by Georg Fischer, Jun 07 2023

Status

approved