

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
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OFFSET

0,2


COMMENTS

The sum of (leftjustified) 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 <= n1), T(n,k) = 12n3k3 (n <= k <= 2n1), 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 pairsums 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



