OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..3321
FORMULA
From Alois P. Heinz, May 23 2024: (Start)
a(n) = Sum_{k=1..n} 2^(k-1) * A066633(n,k).
a(n) mod 2 = A365410(n-1) for n>=1. (End)
EXAMPLE
The partitions of 4 are (4), (3,1), (2,2), (2,1,1), (1,1,1,1), with respective binary ranks 8, 5, 4, 4, 4 with sum 25, so a(4) = 25.
MAPLE
b:= proc(n, i) option remember; `if`(n=0 or i=1, [1, n],
b(n, i-1)+(p->[0, p[1]*2^(i-1)]+p)(b(n-i, min(n-i, i))))
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)]&/@IntegerPartitions[n]], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 23 2024
STATUS
approved