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Maximum number of "feasible" partitions of length n.
10

%I #31 Apr 17 2016 11:50:57

%S 1,1,3,12,140,3950,263707,42285095,16825391023,17095967464466,

%T 45375565948693336

%N Maximum number of "feasible" partitions of length n.

%C a(n) gives the highest value in the (3^(n-1)+1)/2-th through the (3^n-1)/2-th terms of the sequence A254296. It lists the highest possible number of "feasible" partitions into n parts.

%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.

%F The first term is 1. For n>=2, a(n) = A254296((3^(n-1)+5)/2).

%e The numbers 2, 3 and 4 are "feasibly" partitionable into 2 parts. Each of them has 1 feasible partitions. So a(2)=1.

%e The numbers 14 to 40 are "feasibly" partitionable into 4 parts. Among them 16, 18, 19 and 22 each has the highest 12 "feasible" partitions. So a(4)=12.

%e The numbers 122 to 364 are "feasibly" partitionable into 6 parts. Among them 124 has the highest 3950 "feasible" partitions. So a(6)=3950.

%Y Cf. A254296, A254430, A254431, A254432, A254435, A254436, A254437, A254438, A254439, A254440, A254442.

%K nonn,more

%O 1,3

%A _Md. Towhidul Islam_, Feb 03 2015

%E a(9) corrected and a(10)-a(11) added by _Md. Towhidul Islam_, Apr 18 2015