A134392 A077028 * A000012, that is Rascal's triangle (as matrix) multiplied by a lower triangular matrix of ones (main diagonal of ones included).

1, 2, 1, 4, 3, 1, 8, 7, 4, 1, 15, 14, 10, 5, 1, 26, 25, 20, 13, 6, 1, 42, 41, 35, 26, 16, 7, 1, 64, 63, 56, 45, 32, 19, 8, 1, 93, 92, 84, 71, 55, 38, 22, 9, 1, 130, 129, 120, 105, 86, 65, 44, 25, 10, 1, 176, 175, 165, 148, 126, 101, 75, 50, 28, 11, 1

Offset: 1

Author

Gary W. Adamson, Oct 23 2007

Keywords

• nonn
• tabl

Comments

Left border = A000125.

Row sums = A134393.

Examples

			First few rows of the triangle:
   1;
   2,  1;
   4,  3,  1;
   8,  7,  4,  1;
  15, 14, 10,  5,  1;
  26, 25, 20, 13,  6,  1;
  42, 41, 35, 26, 16,  7,  1;
  ...
		

Crossrefs

Cf. A077028, A000125, A134393.

Programs

Mathematica

rows = 11;
R[n_, k_] /; k <= n := k (n - k) + 1; R[0, 0] = 1; R[, ] = 0;
MR = Table[R[n, k], {n, 0, rows-1}, {k, 0, rows-1}];
MB = Table[Boole[0 <= k <= n], {n, 0, rows-1}, {k, 0, rows -1}];
T = MR.MB;
Table[T[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Apr 01 2020 *)

Formula

A077028 * A000012 as infinite lower triangular matrices.

Triangle read by rows, partial sums starting from the right of A077028.

Extensions

Typos corrected by Jean-François Alcover, Apr 01 2020