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

1,2

Comments

Left border = A000125.

Row sums = A134393.

Links

Table of n, a(n) for n=1..66.

Formula

A077028 * A000012 as infinite lower triangular matrices.

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

Example

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;
  ...

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 *)

Crossrefs

Cf. A077028, A000125, A134393.

Sequence in context: A347633 A115450 A109435 * A048483 A276562 A055248

Adjacent sequences: A134389 A134390 A134391 * A134393 A134394 A134395

Keyword

nonn,tabl

Author

Gary W. Adamson, Oct 23 2007

Extensions

Typos corrected by Jean-François Alcover, Apr 01 2020

Status

approved