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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 (list; graph; refs; listen; history; text; internal format)
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, 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
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

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Last modified May 27 17:52 EDT 2024. Contains 372880 sequences. (Running on oeis4.)