OFFSET
1,3
COMMENTS
As described in A254296, all the 'feasible' partitions of natural numbers (3^(n-1)+1)/2 to (3^n-1)/2 has n parts. A254439 lists the "median of the range ((3^(n-1)+1)/2)-th to ((3^n-1)/2)-th terms of A254296".
From conjectured formula, it appears that next terms are 1107102779611719118, 11090084422457163934046, 302002529294596303158583642. - Benedict W. J. Irwin, Nov 16 2016
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.
FORMULA
a(n) = A254296(3^(n-1)).
Conjecture: for n>3, a(n+3) = Sum_{i_1=1..2} Sum_{i_2=1..3*i_1-1} ... Sum_{i_n..3*i_(n-1)-1} (3*i_n - 1). - Benedict W. J. Irwin, Nov 16 2016
EXAMPLE
MATHEMATICA
F[a_, x_, k_] := Sum[x, {a, 1, k}]
F[i1, 3*i1 - 1, 2]
F[i1, F[i2, 3*i2 - 1, 3*i1 - 1], 2]
F[i1, F[i2, F[i3, 3*i3 - 1, 3*i2 - 1], 3*i1 - 1], 2]
F[i1, F[i2, F[i3, F[i4, 3*i4 - 1, 3*i3 - 1], 3*i2 - 1], 3*i1 - 1], 2] (* Examples of how to get first few terms, use the C code to generate the n-th term of the conjectured formula, Benedict W. J. Irwin, Nov 16 2016 *)
PROG
(C)
/* C Code to make Mathematica Code for conjectured n-th term n>3 */
#include <stdio.h>
int main(int argc, char* argv[]){
int i, n=atoi(argv[1])-3;
printf("F[a_, x_, k_]:=Sum[x, {a, 1, k}]\n");
for(i=1; i<=n; i++)printf("F[i%d, ", i);
printf("3i%d-1, ", n);
for(i=n-1; i>0; i--)printf("3i%d-1], ", i);
printf("2]\n");
return 0;
}
/* _Benedict Irwin_, Nov 16 2016 */
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Md. Towhidul Islam, Mar 01 2015
STATUS
approved