A131422 (A000012 * A127773) + (A127773 * A000012) - A000012.

1, 3, 5, 6, 8, 11, 10, 12, 15, 19, 15, 17, 20, 24, 29, 21, 23, 26, 30, 35, 41, 28, 30, 33, 37, 42, 48, 55, 36, 38, 41, 45, 50, 56, 63, 71, 45, 47, 50, 54, 59, 65, 72, 80, 89, 55, 57, 60, 64, 69, 75, 82, 90, 99, 109

Offset: 1

Author

Gary W. Adamson, Jul 10 2007

Keywords

• nonn
• tabl

Comments

Left border = the triangular series, A000217. Right border = A028387, (1, 5, 11, 19, 29, 41, 55, 71, ...). Row sums = A131423: (1, 8, 25, 56, 105, 176, 273, ...).

Examples

			First few rows of the triangle are:
   1;
   3,  5;
   6,  8, 11;
  10, 12, 15, 19;
  15, 17, 20, 24, 29;
  21, 23, 26, 30, 35, 41;
  28, 30, 33, 37, 42, 48, 55;
  ...
		

Crossrefs

Cf. A127773, A000217, A028387, A131423.

Programs

Maple

T:=proc(n,k) options operator, arrow: (1/2)*n*(n+1)+(1/2)*k*(k+1)-1 end proc: for n to 10 do seq(T(n,k),k=1..n) end do; # yields sequence in triangular form - Emeric Deutsch, Sep 06 2008

Formula

(A000012 * A127773) + (A127773 * A000012) - A000012 as infinite lower triangular matrices.

T(n,k) = (n^2 + n + k^2 + k - 2)/2 (1 <= k <= n). - Emeric Deutsch, Sep 06 2008