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

0,2

Comments

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

Row sums = heptagonal pyramidal numbers, A002413.

Links

Table of n, a(n) for n=0..65.

Example

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;
  ...

Prog

(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

Crossrefs

Cf. A000326, A094727, A002413.

Sequence in context: A141234 A130180 A245288 * A300940 A131939 A205522

Adjacent sequences: A104584 A104585 A104586 * A104588 A104589 A104590

Keyword

nonn,tabl

Author

Gary W. Adamson, Mar 17 2005

Extensions

More terms from Michel Marcus, Mar 03 2014

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

Status

approved