OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..5000
EXAMPLE
For n = 4 there are 2 partitions into distinct parts in binary they are: 100, 11+1, for a total of 6 binary parts.
MAPLE
h:= proc(n) option remember; 1+ilog2(n) end:
b:= proc(n, i) option remember; `if`(n=0, [1, 0],
`if`(n>i*(i+1)/2, 0, b(n, i-1)+(p-> p+h(i)
*[0, p[1]])(b(n-i, min(n-i, i-1)))))
end:
a:= n-> b(n$2)[2]:
seq(a(n), n=1..60); # Alois P. Heinz, Sep 27 2018
MATHEMATICA
h[n_] := h[n] = 1+Log[2, n] // Floor;
b[n_, i_] := b[n, i] = If[n == 0, {1, 0}, If[n > i*(i+1)/2, 0, b[n, i-1] + Function[p, p + h[i]*{0, p[[1]]}][b[n-i, Min[n-i, i-1]]]]];
a[n_] := b[n, n][[2]];
a /@ Range[1; 60] (* Jean-François Alcover, Sep 28 2019, after Alois P. Heinz *)
PROG
(PARI) seq(n)={[subst(deriv(p, y), y, 1) | p<-Vec(-1 + prod(k=1, n, 1 + x^k*y^(logint(k, 2)+1) + O(x*x^n)))]} \\ Andrew Howroyd, Sep 17 2018
CROSSREFS
KEYWORD
nonn,base
AUTHOR
David S. Newman, Sep 11 2018
STATUS
approved