

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.


3



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
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OFFSET

0,3


LINKS



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, i1)+`if`(a(i)>n, 0, b(na(i), i1))))
end:
a:= proc(n) a(n):= `if`(n<2, 1, b(n1, n1)) end:


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]];


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



