A254433 Maximum number of "feasible" partitions of length n.

1, 1, 3, 12, 140, 3950, 263707, 42285095, 16825391023, 17095967464466, 45375565948693336

Offset: 1

Author

Md. Towhidul Islam, Feb 03 2015

Keywords

• nonn
• more

Comments

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.

Examples

			The numbers 2, 3 and 4 are "feasibly" partitionable into 2 parts. Each of them has 1 feasible partitions. So a(2)=1.
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.
The numbers 122 to 364 are "feasibly" partitionable into 6 parts. Among them 124 has the highest 3950 "feasible" partitions. So a(6)=3950.
		

Links

• Md Towhidul Islam & Md Shahidul Islam, 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, arXiv:1502.07730 [math.CO], 2015.

Crossrefs

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

Formula

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

Extensions

a(9) corrected and a(10)-a(11) added by Md. Towhidul Islam, Apr 18 2015