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

0,2

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.

Links

Table of n, a(n) for n=0..63.

Formula

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

Example

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.

Maple

See A245556.

Crossrefs

Partial sums of the rows gives A245556.

Row sums are A082040.

Sequence in context: A321872 A221363 A245943 * A197071 A231737 A140072

Adjacent sequences: A245554 A245555 A245556 * A245558 A245559 A245560

Keyword

nonn,tabf

Author

N. J. A. Sloane, Aug 04 2014

Status

approved