A022541 Related to number of irreducible stick-cutting problems.

0, 0, 0, 1, 1, 1, 4, 7, 9, 21, 41, 73, 147, 288, 557, 1111, 2193, 4343, 8728, 17483, 35063, 70828, 143267, 290193, 589705, 1200646, 2448904, 5005001, 10245216, 21005238, 43134355, 88696073, 182621943, 376496023, 777098691, 1605731742, 3321492918, 6877489184

Offset: 1

Author

Frans J. Faase

Keywords

• nonn

Comments

Number of partitions of n(n+1)/2 with all elements greater than n and less than 2n-1. - David Bevan, Sep 19 2011

Examples

			a(4)=1: 10 can be partitioned as (5,5). - _David Bevan_, Sep 19 2011
		

Links

• F. Faase, The cutting sticks problem
• Mathematics Stack Exchange, Cutting sticks puzzle

Programs

Mathematica

Table[Length[IntegerPartitions[n(n+1)/2, All, Range[n+1,2n-2]]], {n, 20}] (* David Bevan, Sep 19 2011 *)

Formula

a(n) = [x^(n*(n+1)/2)] Product_{k=n+1..2*n-2} 1/(1-x^k). - Sean A. Irvine, May 18 2019

Extensions

a(4) and a(5) corrected by David Bevan, Sep 19 2011

More terms from Alois P. Heinz, Sep 20 2012