A113125 A simple tridiagonal matrix.

1, 1, 2, 1, 2, 3, 0, 2, 3, 4, 0, 0, 3, 4, 5, 0, 0, 0, 4, 5, 6, 0, 0, 0, 0, 5, 6, 7, 0, 0, 0, 0, 0, 6, 7, 8, 0, 0, 0, 0, 0, 0, 7, 8, 9, 0, 0, 0, 0, 0, 0, 0, 8, 9, 10, 0, 0, 0, 0, 0, 0, 0, 0, 9, 10, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 11, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 12, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Paul Barry, Oct 14 2005

Keywords

• easy
• nonn
• tabl

Comments

Row sums are A008486 (coordination sequence for graphite net). Diagonal sums are A026741(n+1). Diagonals are A000027.

Examples

			Triangle begins
  1;
  1, 2;
  1, 2, 3;
  0, 2, 3, 4;
  0, 0, 3, 4, 5;
  0, 0, 0, 4, 5, 6;
  0, 0, 0, 0, 5, 6, 7;
  0, 0, 0, 0, 0, 6, 7, 8;
		

Crossrefs

Cf. A113126.

Programs

Mathematica

Table[If[#<(n-2),0,#]&/@Range[n],{n,15}]//Flatten (* Harvey P. Dale, Oct 14 2022 *)

Formula

Number triangle where column k has g.f. (1+x+x^2)(k+1)x^k.