A162932 a(n) = A053445(n-2) - A053445(n-4).
1, 0, 1, 1, 1, 1, 3, 1, 3, 4, 4, 4, 8, 6, 10, 11, 13, 15, 22, 20, 28, 33, 39, 43, 58, 60, 77, 88, 104, 119, 148, 160, 197, 226, 265, 300, 363, 404, 481, 549, 638, 727, 858, 961, 1126, 1283, 1480, 1680, 1953, 2201, 2544, 2887, 3309, 3750, 4312, 4857, 5566, 6301, 7175
Offset: 6
Keywords
Examples
For n = 19 the a(19) = 6 partitions are 5554, 44443, 55522, 444322, 3333322 and 33322222.
Links
- Andrew van den Hoeven, Table of n, a(n) for n = 6..10000
Programs
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Magma
a:=func
; [a(n): n in [6..100]]; // Vincenzo Librandi, Dec 09 2014 -
Mathematica
Table[PartitionsP[n] - 2 PartitionsP[n - 1] + 2 PartitionsP[n - 3] - PartitionsP[n - 4], {n, 6, 70}] (* Vincenzo Librandi, Dec 09 2014 *)
Formula
From Mircea Merca, Jun 11 2012: (Start)
a(n) = p(n) - 2*p(n-1) + 2*p(n-3) - p(n-4) for n >= 6, where p(n) = A000041(n).
G.f.: -1 + x - x^3 + (1 - x)*Product_{k > 2} 1/(1 - x^k). (End)
a(n) ~ exp(Pi*sqrt(2*n/3)) * Pi^3 / (36*sqrt(2)*n^(5/2)). - Vaclav Kotesovec, Jun 02 2018
G.f.: Sum_{n >= 1} q^(3*n+3)/Product_{k = 1..n} 1 - q^(k+1). - Peter Bala, Dec 01 2024
Extensions
Keyword:tabf removed, indexing corrected, sequence extended by R. J. Mathar, Sep 17 2009
Comments