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

Author

Gary W. Adamson, Jun 16 2007

Keywords

• nonn
• tabl

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.

Examples

			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;
  ...
		

Links

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

Crossrefs

Cf. A007318, A097806, A151821, A167374.

Programs

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 *)

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