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

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

Offset

1,3

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.

Links

Table of n, a(n) for n=1..11.

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.

Formula

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

Example

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.

Crossrefs

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

Sequence in context: A056417 A363412 A322227 * A285603 A329471 A098152

Adjacent sequences: A254430 A254431 A254432 * A254434 A254435 A254436

Keyword

nonn,more

Author

Md. Towhidul Islam, Feb 03 2015

Extensions

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

Status

approved