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%I #21 Aug 05 2014 13:34:39
%S 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,
%T 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,
%U 15,18,21,60,57,54,51,48,45,42,22
%N 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.
%C 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.
%F T(n,k) = 3k (0 <= k <= n-1), T(n,k) = 12n-3k-3 (n <= k <= 2n-1), T(n,2n) = 3n+1.
%e Triangle begins:
%e [1]
%e [3, 6, 4]
%e [3, 6, 15, 12, 7]
%e [3, 6, 9, 24, 21, 18, 10]
%e [3, 6, 9, 12, 33, 30, 27, 24, 13]
%e [3, 6, 9, 12, 15, 42, 39, 36, 33, 30, 16]
%e [3, 6, 9, 12, 15, 18, 51, 48, 45, 42, 39, 36, 19]
%e [3, 6, 9, 12, 15, 18, 21, 60, 57, 54, 51, 48, 45, 42, 22]
%e ...
%e Example. Suppose n = 2. We find:
%e triple count pair-sums 0 1 2 3 4
%e -------------
%e 002 3 0,2 3 3
%e 012 6 1,2,3 6 6 6
%e 112 3 2,3 3 3
%e 022 3 2,4 3 3
%e 122 3 3,4 3 3
%e 222 1 4 1
%e -------------
%e Totals: 3 6 15 12 7, which is row 2 of the triangle.
%p See A245556.
%Y Partial sums of the rows gives A245556.
%Y Row sums are A082040.
%K nonn,tabf
%O 0,2
%A _N. J. A. Sloane_, Aug 04 2014
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