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A254439 Median of terms of A254296 in the range (3^(n-1)+1)/2 to (3^n-1)/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^(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

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) = 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

As described in sequence A254296, "feasible" partitions of the integers 41 through 121 consist of 5 parts. The number 3^(5-1) = 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 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

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

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Last modified July 16 09:13 EDT 2020. Contains 335784 sequences. (Running on oeis4.)