A104587 Triangle read by rows, given by the matrix product A * B where A (A094727) = [1; 2, 3; 3, 4, 5; 4, 5, 6, 7; ...] and B = [1; 1, 1; 1, 1, 1; ...] (both are infinite lower triangular matrices with the other terms zero).

1, 5, 3, 12, 9, 5, 22, 18, 13, 7, 35, 30, 24, 17, 9, 51, 45, 38, 30, 21, 11, 70, 63, 55, 46, 36, 25, 13, 92, 84, 75, 65, 54, 42, 29, 15, 117, 108, 98, 87, 75, 62, 48, 33, 17, 145, 135, 124, 112, 99, 85, 70, 54, 37, 19, 176, 165, 153, 140, 126, 111, 95, 78, 60, 41, 21

Offset: 0

Author

Gary W. Adamson, Mar 17 2005

Keywords

• nonn
• tabl

Comments

Left column of the triangle = pentagonal numbers, A000326 (starting with 1).

Row sums = heptagonal pyramidal numbers, A002413.

Examples

			Triangle begins:
   1;
   5,  3;
  12,  9,  5;
  22, 18, 13,  7;
  35, 30, 24, 17,  9;
  51, 45, 38, 30, 21, 11;
  70, 63, 55, 46, 36, 25, 13;
  92, 84, 75, 65, 54, 42, 29, 15;
  ...
		

Crossrefs

Cf. A000326, A094727, A002413.

Programs

PARI

tabl(nn) = {ma = matrix(nn, nn, n, k, (n+k-1)*(k<=n)); mb = matrix(nn, nn, n, k, (k<=n)); mt = ma*mb; for (i=1, nn, for (j=1, i, print1(ma[i,j], ", ");); print(););} \\ Michel Marcus, Mar 03 2014

Extensions

More terms from Michel Marcus, Mar 03 2014

Edited by Michel Marcus and N. J. A. Sloane, Mar 03 2014