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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 11 23:44 EST 2019. Contains 329945 sequences. (Running on oeis4.)