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%I #13 Apr 17 2016 11:52:24
%S 1,4,1,1,19,7,10,3,3,2,2,1,1,201,62,124,27,37,35,42,31,35,16,16,14,14,
%T 12,12,9,9,7,7,5,5,3,3,2,2,1,1,5020,1271,3551,431,719,840,1128,851,
%U 1051,255,303,327,369,370,408,358,387,340,366,309,330,262,280,248,264,226,238,183,183,173,173,162,162,150,150
%N Triangle read by rows: T(n,k) is the total number of parts of denomination k used in all n-part feasible partitions described in A254296.
%C Row n contains 3^(n-1) terms.
%C Sum of row n equals n*A254430(n).
%H Md. Towhidul Islam, <a href="/A254442/b254442.txt">Table of n, a(n) for n = 1..364</a>
%H Md Towhidul Islam & Md Shahidul Islam, <a href="http://arxiv.org/abs/1502.07730">Number of Partitions of an n-kilogram Stone into Minimum Number of Weights to Weigh All Integral Weights from 1 to n kg(s) on a Two-pan Balance</a>, arXiv:1502.07730 [math.CO], 2015.
%e Triangle begins:
%e 1;
%e 4, 1, 1;
%e 19, 7, 10, 3, 3, 2, 2, 1, 1;
%e 201, 62, 124, 27, 37, 35, 42, 31, 35, 16, 16, 14, 14, 12, 12, 9, 9, 7, 7, 5, 5, 3, 3, 2, 2, 1, 1;
%e 5020, 1271, 3551, 431, 719, 840, 1128, 851, 1051, 255, 303, 327, 369, 370, 408, 358, 387, 340, 366, 309, 330, 262, 280, 248, 264, 226, 238, 183, 183, 173, 173, 162, 162, 150, 150, 139, 139, 127, 127, 115, 115, 104, 104, 93, 93, 81, 81, 72, 72, 63, 63, 54, 54, 47, 47, 40, 40, 33, 33, 28, 28, 23, 23, 18, 18, 15, 15, 12, 12, 9, 9, 7, 7, 5, 5 ,3, 3, 2, 2, 1, 1;
%Y Cf. A254296, A254431, A254432, A254433, A254435, A254436, A254437, A254438, A254439, A254440.
%K nonn,look,tabf
%O 1,2
%A _Md. Towhidul Islam_, May 12 2015
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