A254430 Number of "feasible" partitions with n parts.

1, 3, 16, 183, 4804, 299558, 45834625, 17696744699, 17644374475261, 46279884666882734, 324101360547203133793

Offset

1,2

Comments

This sequence answers the question: "How many sellers can each be provided with a distinct set of n-part 'feasible' weights described in A254296?" It counts all the n-part "feasible" partitions of all the natural numbers from (3^(n-1)+1)/2 to (3^n-1)/2. Here n resembles m in A254296.

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

a(n) = Sum_{p=(3^(n-1)+1)/2..(3^n-1)/2} A254296(p).

Example

For n=2, we count 2nd through 4th values of A254296. So a(2)=1+1+1=3.
For n=3, we count 5th through 13th values from A254296. So a(3)= 2+2+3+2+2+2+1+1+1 = 16.
For n=4, a(4)= Sum of 14th through 40th terms of A254296, that is, 183.

Mathematica

okQ[v_] := Module[{s = 0}, For[i = 1, i <= Length[v], i++, If[v[[i]] > 2s + 1, Return[False], s += v[[i]]]]; Return[True]];
a254296[n_] := With[{k = Ceiling[Log[3, 2n]]}, Select[Reverse /@ IntegerPartitions[n, {k}], okQ] // Length];
a[n_] := Sum[a254296[p], {p, (3^(n-1) + 1)/2, (3^n - 1)/2}];
Array[a, 5] (* Jean-François Alcover, Nov 04 2018, after Charles R Greathouse IV in A254296 *)

Crossrefs

Cf. A254296, A254431, A254432, A254433, A254435, A254436, A254437, A254438, A254439, A254440, A254442.

Sequence in context: A304902 A024041 A152554 * A180721 A192668 A045990

Adjacent sequences: A254427 A254428 A254429 * A254431 A254432 A254433

Keyword

nonn

Author

Md. Towhidul Islam, Jan 30 2015

Extensions

a(9)-a(11) from Md. Towhidul Islam, Apr 18 2015

Status

approved