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A254442 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.

%I A254442 #13 Apr 17 2016 11:52:24
%S A254442 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 A254442 12,12,9,9,7,7,5,5,3,3,2,2,1,1,5020,1271,3551,431,719,840,1128,851,
%U A254442 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 A254442 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 A254442 Row n contains 3^(n-1) terms.
%C A254442 Sum of row n equals n*A254430(n).
%H A254442 Md. Towhidul Islam, <a href="/A254442/b254442.txt">Table of n, a(n) for n = 1..364</a>
%H A254442 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 A254442 Triangle begins:
%e A254442 1;
%e A254442 4, 1, 1;
%e A254442 19, 7, 10, 3, 3, 2, 2, 1, 1;
%e A254442 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 A254442 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 A254442 Cf. A254296, A254431, A254432, A254433, A254435, A254436, A254437, A254438, A254439, A254440.
%K A254442 nonn,look,tabf
%O A254442 1,2
%A A254442 _Md. Towhidul Islam_, May 12 2015