

A022541


Related to number of irreducible stickcutting problems.


0



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,7


COMMENTS

Number of partitions of n(n+1)/2 with all elements greater than n and less than 2n1.  David Bevan, Sep 19 2011


LINKS

Table of n, a(n) for n=1..38.
F. Faase, The cutting sticks problem
StackExchange, Cutting sticks puzzle


FORMULA

a(n) = [x^(n*(n+1)/2] Product_{k=n+1..2*n2} 1/(1x^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, 2n2]]], {n, 20}] (* David Bevan, Sep 19 2011 *)


CROSSREFS

Sequence in context: A121865 A103073 A166742 * 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



