A254431 Number of "feasible" partitions of the smallest natural number of length n.

1, 1, 2, 10, 131, 3887, 262555, 42240104, 16821037273, 17094916187012, 45374905859155948

Offset: 1

Author

Md. Towhidul Islam, Jan 30 2015

Keywords

• nonn
• more

Comments

The sequence lists the number of "feasible" partitions of the first natural number (3^(n-1)+1)/2 of length n. Here n resembles m in A254296 which describes "feasible" partitions.

Examples

			The smallest natural numbers "feasibly" partitionable into 1, 2, 3, 4 and 5 parts respectively are 1,2,5,14 and 41. From A254296, the number of "feasible" partitions of them are 1,1,2,10 and 131.
		

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, A254432, A254433, A254435, A254436, A254437, A254438, A254439, A254440, A254442.

Formula

a(n) = A254296((3^(n-1)+1)/2).

Extensions

a(10)-a(11) from Md. Towhidul Islam, Apr 18 2015