OFFSET
1,2
COMMENTS
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) = Sum_{p=(3^(n-1)+1)/2..(3^n-1)/2} A254296(p).
EXAMPLE
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}];
CROSSREFS
KEYWORD
nonn
AUTHOR
Md. Towhidul Islam, Jan 30 2015
EXTENSIONS
a(9)-a(11) from Md. Towhidul Islam, Apr 18 2015
STATUS
approved