OFFSET
0,3
COMMENTS
Generalization of Adams-Watters's criterion for complete partitions, that each part is no more than 1 more than the sum of all smaller parts.
Also the number of complete partitions of n+1 that contain more than one 1. - George Beck, Oct 01 2017
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
FORMULA
a(n) ~ exp(Pi*sqrt(2*n/3)) / (4*sqrt(3)*n). - Vaclav Kotesovec, May 24 2018
EXAMPLE
For n = 8, a(8) = 17 counts all partitions of 8 except (8), (7,1), (6,2), (6,1,1), and (4,4).
MATHEMATICA
Table[Count[IntegerPartitions@ n, w_ /; And[Last@ w <= 3, NoneTrue[w - Rest@ PadRight[3 + Reverse@ Accumulate@ Reverse@ w, Length@ w + 1, Last@ w], # > 0 &]]], {n, 50}] (* Michael De Vlieger, May 16 2017, Version 10 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Brian Hopkins, May 16 2017
STATUS
approved