OFFSET
0,8
COMMENTS
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
G. E. Andrews, M. Beck and N. Robbins, Partitions with fixed differences between largest and smallest parts, arXiv:1406.3374 [math.NT], 2014
FORMULA
Conjecture. a(1)=0 and, for n>1, a(n+1)=a(n)+d(n), where d(n) is defined as follows: d=0,0,0,1,0 for n=1,...,5 and, for n>5, d(n)=d(n-2)+1 if n=6k or n=6k+4, d(n)=d(n-2) if n=6k+1 or n=6k+3, d(n)=d(n-2)+2Floor[n/6] if n=6k+2 and d(n)=d(n-5) if n=6k+5.
G.f. for number of partitions p of n such that max(p)-min(p) = m is Sum_{k>0} x^(2*k+m)/Product_{i=0..m} (1-x^(k+i)). - Vladeta Jovovic, Jul 04 2007
MATHEMATICA
np[n_]:=Length[Select[IntegerPartitions[n], Max[#]-Min[#]==3&]]; Array[np, 60] (* Harvey P. Dale, Jul 02 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
John W. Layman, May 07 2007
EXTENSIONS
More terms from Vladeta Jovovic, Jul 04 2007
STATUS
approved