A254436 A component sequence of A254296.

0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 4, 3, 6, 3, 6, 5, 8, 7, 10, 7, 12, 9, 14, 11, 16, 14, 19, 17, 22, 20, 28, 23, 31, 26, 34, 32, 40, 35, 43, 38, 51, 46, 59, 51, 64, 61, 74, 71, 84, 76, 94, 86, 104, 96, 114, 108, 126, 120, 138, 132, 157, 146, 171

Offset

1,13

Comments

This sequence is a component of the formula for counting A254296.

If m=ceiling(log_3(2k)), define n=(3^(m-1)+1)/2+(3^(m-2))-k for k in the range (3^(m-1)+1)/2<=k<=(3^(m-1)-1)/2+(3^(m-2)). Then this sequence gives the first 3^(m-2) terms.

Links

Md. Towhidul Islam, Table of n, a(n) for n = 1..6561

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

If m=ceiling(log_3(2k)), define n=(3^(m-1)+1)/2+(3^(m-2))-k for k in the range (3^(m-1)+1)/2<=k<=(3^(m-1)-1)/2+(3^(m-2)).

Then a(n)=Sum_{d=ceiling((3k+2)/5)..(3^(m-1)-1)/2} Sum_{p=ceiling((d-1)/3..2d-k-1} A254296(p).

Crossrefs

Cf. A254296, A254430, A254431, A254432, A254433, A254435, A254437, A254438, A254439, A254440.

Sequence in context: A344257 A088931 A088980 * A208548 A157333 A002852

Adjacent sequences: A254433 A254434 A254435 * A254437 A254438 A254439

Keyword

nonn

Author

Md. Towhidul Islam, Feb 28 2015

Status

approved