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

1,7

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

Links

Table of n, a(n) for n=1..38.

F. Faase, The cutting sticks problem

Mathematics Stack Exchange, Cutting sticks puzzle

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

Example

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

Mathematica

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

Crossrefs

Sequence in context: A103073 A166742 A346554 * A330695 A063798 A084035

Adjacent sequences: A022538 A022539 A022540 * A022542 A022543 A022544

Keyword

nonn

Author

Frans J. Faase

Extensions

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

More terms from Alois P. Heinz, Sep 20 2012

Status

approved