

A254439


Median of terms of A254296 in the range (3^(n1)+1)/2 to (3^n1)/2.


11



1, 1, 2, 7, 47, 682, 23132, 1913821, 397731998, 212521309666, 297464368728296
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

As described in A254296, all the 'feasible' partitions of natural numbers (3^(n1)+1)/2 to (3^n1)/2 has n parts. A254439 lists the "median of the range ((3^(n1)+1)/2)th to ((3^n1)/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

Table of n, a(n) for n=1..11.
Md Towhidul Islam & Md Shahidul Islam, Number of Partitions of an nkilogram Stone into Minimum Number of Weights to Weigh All Integral Weights from 1 to n kg(s) on a Twopan Balance, arXiv:1502.07730 [math.CO], 2015.


FORMULA

a(n) = A254296(3^(n1)).
Conjecture: for n>3, a(n+3) = Sum_{i_1=1..2} Sum_{i_2=1..3*i_11} ... Sum_{i_n..3*i_(n1)1} (3*i_n  1).  Benedict W. J. Irwin, Nov 16 2016


EXAMPLE

As described in sequence A254296, "feasible" partitions of the integers 41 through 121 consist of 5 parts. The number 3^(51) = 81 has 47 "feasible" partitions, which is the median of the range from the 41st to the 121st term of A254296.


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 nth term of the conjectured formula, Benedict W. J. Irwin, Nov 16 2016 *)


PROG

(C)
/* C Code to make Mathematica Code for conjectured nth 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%d1, ", n);
for(i=n1; i>0; i)printf("3i%d1], ", i);
printf("2]\n");
return 0;
}
/* _Benedict Irwin_, Nov 16 2016 */


CROSSREFS

Cf. A254296, A254430, A254431, A254432, A254433, A254435, A254436, A254437, A254438, A254440.
Sequence in context: A117141 A305533 A125813 * A106159 A160915 A330474
Adjacent sequences: A254436 A254437 A254438 * A254440 A254441 A254442


KEYWORD

nonn,more


AUTHOR

Md. Towhidul Islam, Mar 01 2015


STATUS

approved



