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A254432 Natural numbers with the maximum number of "feasible" partitions of length m. 9
1, 2, 3, 4, 7, 16, 18, 19, 22, 43, 46, 124, 367, 1096, 3283, 9844, 29527, 88576, 265723, 797164, 2391487, 7174456, 21523363, 64570084, 193710247, 581130736, 1743392203, 5230176604 (list; graph; refs; listen; history; text; internal format)



Sequence A254296 describes "feasible" partitions and gives the number of all "feasible" partitions of all natural numbers. We must take the value of m from there.

Here we list the natural numbers with the highest number of "feasible" partitions of length m. Such numbers are unique for all m except for m=[2,4,5].

For m>=6, there is a unique natural number with the maximum number of "feasible" partitions.


Table of n, a(n) for n=1..28.

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.


For the first 11 values, there is no specific formula.

For n>=12, a(n) = (3^(m-7)+5)/2.

Recursively, for n>=13, a(n) = 3*a(n-1)-5.


Natural numbers with maximum "feasible" partitions are unique for all m except for m=[2,4,5].

For m=1, the number 1 has 1 "feasible" partition.

For m=2, three numbers 2,3 and 4 each has the highest 1 "feasible" partition.

For m=3, the number 7 has the highest 3 "feasible" partitions.

For m=4, four numbers 16,18,19 and 22 each has the highest 12 "feasible" partitions.

For m=5, two numbers 43 and 46 each has 140 "feasible" partitions.

For m=6, the number 124 has the highest 3950 "feasible" partitions.

For m=7, the number 367 has the highest 263707 "feasible" partitions.

For m=8, the number 1096 has the highest 42285095 "feasible" partitions.


Cf. A254296, A254430, A254431, A254433, A254435, A254436, A254437, A254438, A254439, A254440, A254442.

Sequence in context: A098010 A088533 A091155 * A027362 A068194 A179985

Adjacent sequences:  A254429 A254430 A254431 * A254433 A254434 A254435




Md. Towhidul Islam, Jan 30 2015



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Last modified May 26 02:56 EDT 2020. Contains 334613 sequences. (Running on oeis4.)