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

0,3

Links

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

Example

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).

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 *)

Crossrefs

Sequence in context: A341731 A183002 A211859 * A294150 A087135 A227135

Adjacent sequences: A057598 A057599 A057600 * A057602 A057603 A057604

Keyword

nonn

Author

Leroy Quet, Oct 06 2000

Extensions

More terms from Naohiro Nomoto, Oct 28 2001

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

Status

approved