cp's OEIS Frontend

A121659 Number of partitions of n into parts with at most one part not greater than 2.

%I A121659 #15 Jan 15 2022 04:29:29
%S A121659 1,1,1,2,3,4,5,7,9,12,15,20,25,32,40,51,63,79,97,121,148,182,221,271,
%T A121659 328,398,479,579,694,834,995,1190,1415,1684,1995,2366,2793,3298,3881,
%U A121659 4569,5360,6288,7355,8603,10037,11705,13619,15842,18388,21333,24703
%N A121659 Number of partitions of n into parts with at most one part not greater than 2.
%C A121659 The number of partitions of n that have the first part at least thrice larger than the second part. Example: a(8) = #{8, 7+1, 6+2, 6+1+1, 5+1+1+1, 4+1+1+1+1, 3+1+1+1+1+1}=7. [_Mircea Merca_, Jul 24 2011]
%H A121659 Vaclav Kotesovec, <a href="/A121659/b121659.txt">Table of n, a(n) for n = 1..10000</a>
%H A121659 Mircea Merca, <a href="https://arxiv.org/abs/1903.10797">Fast algorithm for generating ascending compositions</a>, arXiv:1903.10797 [math.CO], 2019.
%F A121659 a(n) = A121081(n) - A008483(n-3) for n>2.
%F A121659 a(n) = p(n) - p(n-2) - p(n-3) + p(n-5) where p(n) = A000041(n). See Merca p. 6. - _Michel Marcus_, Mar 27 2019
%F A121659 a(n) ~ exp(Pi*sqrt(2*n/3)) * Pi^2 / (4*sqrt(3)*n^2) * (1 - (18/Pi + 61*Pi/24)/sqrt(6*n)). - _Vaclav Kotesovec_, Jan 15 2022
%e A121659 a(8) = #{8,7+1,6+2,5+3,4+4,4+3+1,3+3+2} = 7;
%e A121659 a(9) = #{9,8+1,7+2,6+3,5+4,5+3+1,4+4+1,4+3+2,3+3+3} = 9.
%Y A121659 Cf. A027336, A008483, A121081, A000041.
%K A121659 nonn
%O A121659 1,4
%A A121659 _Reinhard Zumkeller_, Aug 14 2006