A066920 Number of partitions of n into lucky parts.

1, 1, 2, 2, 2, 3, 4, 4, 6, 7, 7, 9, 11, 12, 15, 18, 19, 23, 26, 28, 34, 39, 42, 49, 56, 60, 69, 79, 85, 97, 110, 118, 133, 150, 162, 181, 203, 219, 243, 271, 292, 323, 359, 387, 425, 471, 507, 554, 612, 659, 719, 791, 851, 924, 1012, 1089, 1179, 1289, 1386, 1497, 1630

Offset

1,3

Links

Table of n, a(n) for n=1..61.

V. Gardiner, R. Lazarus, N. Metropolis, and S. Ulam, On certain sequences of integers defined by sieves, Mathematics Magazine, 29(3) (1955), 117-122.

OEIS, Lucky numbers.

Hugo van der Sanden, C code to calculate lucky numbers for A000959.

Eric Weisstein's World of Mathematics, Lucky number.

Wikipedia, Lucky number.

Example

a(7) = 4 because we have the following partitions of n = 7 into lucky numbers: 7 = 3 + 3 + 1 = 3 + 1 + 1 + 1 + 1 = 1 + 1 + 1 + 1 + 1 + 1 + 1. - Petros Hadjicostas, Jun 05 2020

Mathematica

lst = Range[1, 100, 2]; i = 2; While[ i <= (len = Length@lst) && (k = lst[[i]]) <= len, lst = Drop[lst, {k, len, k}]; i++ ]; Rest@ CoefficientList[Series[1/Times @@ (1 - x^lst), {x, 0, 61}], x] (* Robert G. Wilson v, May 12 2006 *)

Crossrefs

Cf. A000959.

Sequence in context: A301337 A302404 A029050 * A035381 A096938 A130084

Adjacent sequences: A066917 A066918 A066919 * A066921 A066922 A066923

Keyword

easy,nonn

Author

Naohiro Nomoto, Jan 26 2002

Extensions

More terms from Robert G. Wilson v, May 12 2006

Status

approved