A057601 a(0) = a(1) = 1; a(n+1) is the number of partitions of n into parts a(k), 0 <= k <= n, each k occurring at most once.

1, 1, 2, 2, 4, 4, 6, 8, 10, 11, 12, 14, 17, 21, 25, 29, 33, 37, 43, 49, 54, 59, 66, 72, 80, 89, 98, 106, 116, 126, 137, 148, 161, 174, 187, 200, 216, 232, 248, 266, 284, 302, 321, 344, 367, 391, 414, 440, 465, 493, 523, 556, 584, 616, 650, 689, 726, 768, 808

Offset: 0

Author

Leroy Quet, Oct 06 2000

Keywords

• nonn

Examples

			a(6) = 6 because 5 = a(0) + a(4) = a(0) + a(5) = a(1) + a(4) = a(1) + a(5) = a(0) + a(2) + a(3) = a(1) + a(2) + a(3).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<0, 0,
       b(n, i-1)+`if`(a(i)>n, 0, b(n-a(i), i-1))))
    end:
a:= proc(n) a(n):= `if`(n<2, 1, b(n-1, n-1)) end:
seq(a(n), n=0..70);  # Alois P. Heinz, May 26 2013

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 0, 0, b[n, i - 1] + If[a[i] > n, 0, b[n - a[i], i - 1]]]];
a[n_] := If[n < 2, 1, b[n - 1, n - 1]];
a /@ Range[0, 70] (* Jean-François Alcover, Nov 10 2020, after Alois P. Heinz *)

Extensions

More terms from Naohiro Nomoto, Oct 28 2001

Extended beyond a(45) by Alois P. Heinz, May 26 2013