OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..3321
FORMULA
a(n) = Sum_{k=1..n} 2^(k-1) * A015716(n,k). - Alois P. Heinz, May 24 2024
EXAMPLE
The strict partitions of 6 are (6), (5,1), (4,2), (3,2,1), with respective binary ranks 32, 17, 10, 7 with sum 66, so a(6) = 66.
MAPLE
b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,
`if`(n=0, [1, 0], b(n, i-1)+ (p-> [0, p[1]*2^(i-1)]
+p)(b(n-i, min(n-i, i-1)))))
end:
a:= n-> b(n$2)[2]:
seq(a(n), n=0..33); # Alois P. Heinz, May 23 2024
MATHEMATICA
Table[Total[Total[2^(#-1)]& /@ Select[IntegerPartitions[n], UnsameQ@@#&]], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 23 2024
STATUS
approved