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Number of partitions of n into lucky parts.
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%I #18 Jun 25 2020 02:06:36

%S 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,

%T 79,85,97,110,118,133,150,162,181,203,219,243,271,292,323,359,387,425,

%U 471,507,554,612,659,719,791,851,924,1012,1089,1179,1289,1386,1497,1630

%N Number of partitions of n into lucky parts.

%H V. Gardiner, R. Lazarus, N. Metropolis, and S. Ulam, <a href="https://www.jstor.org/stable/3029719">On certain sequences of integers defined by sieves</a>, Mathematics Magazine, 29(3) (1955), 117-122.

%H OEIS, <a href="http://oeis.org/wiki/Lucky_numbers">Lucky numbers</a>.

%H Hugo van der Sanden, <a href="https://github.com/hvds/seq/tree/master/lucky">C code to calculate lucky numbers for A000959</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LuckyNumber.html">Lucky number</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Lucky_number">Lucky number</a>.

%e 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

%t 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 *)

%Y Cf. A000959.

%K easy,nonn

%O 1,3

%A _Naohiro Nomoto_, Jan 26 2002

%E More terms from _Robert G. Wilson v_, May 12 2006