A245557 Irregular triangle read by rows: T(n,k) (n>=0, 0 <= k <= 2n) = number of triples (u,v,w) with entries in the range 0 to n which have some pair adding up to k and in which at least one of u,v,w is equal to n.

1, 3, 6, 4, 3, 6, 15, 12, 7, 3, 6, 9, 24, 21, 18, 10, 3, 6, 9, 12, 33, 30, 27, 24, 13, 3, 6, 9, 12, 15, 42, 39, 36, 33, 30, 16, 3, 6, 9, 12, 15, 18, 51, 48, 45, 42, 39, 36, 19, 3, 6, 9, 12, 15, 18, 21, 60, 57, 54, 51, 48, 45, 42, 22

Offset: 0

Author

N. J. A. Sloane, Aug 04 2014

Keywords

• nonn
• tabf

Comments

The sum of (left-justified) rows 0 through n gives row n of A245556. For example, the sum of rows 0 thru 2 is 7, 12, 19, 12, 7, which is the n=2 row of A245556.

Examples

			Triangle begins:
[1]
[3, 6, 4]
[3, 6, 15, 12, 7]
[3, 6, 9, 24, 21, 18, 10]
[3, 6, 9, 12, 33, 30, 27, 24, 13]
[3, 6, 9, 12, 15, 42, 39, 36, 33, 30, 16]
[3, 6, 9, 12, 15, 18, 51, 48, 45, 42, 39, 36, 19]
[3, 6, 9, 12, 15, 18, 21, 60, 57, 54, 51, 48, 45, 42, 22]
...
Example. Suppose n = 2. We find:
triple count pair-sums 0  1  2  3  4
                       -------------
002      3     0,2     3     3
012      6     1,2,3      6  6  6
112      3     2,3           3  3
022      3     2,4           3     3
122      3     3,4              3  3
222      1     4                   1
                       -------------
Totals:                3  6 15 12  7, which is row 2 of the triangle.
		

Crossrefs

Partial sums of the rows gives A245556.

Row sums are A082040.

Programs

Maple

See A245556.

Formula

T(n,k) = 3k (0 <= k <= n-1), T(n,k) = 12n-3k-3 (n <= k <= 2n-1), T(n,2n) = 3n+1.