login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A209038 Number of partitions of n into parts not less than max(1,n/4). 3

%I #8 Jul 13 2013 12:04:23

%S 1,1,2,3,5,7,11,15,7,8,12,14,9,10,13,17,11,12,16,18,13,15,18,21,16,17,

%T 21,24,18,20,24,27,21,23,27,30,24,26,30,34,27,29,34,37,30,33,37,41,34,

%U 36,41,45,37,40,45,49,41,44,49,53,45,48,53,58,49,52,58

%N Number of partitions of n into parts not less than max(1,n/4).

%H Reinhard Zumkeller, <a href="/A209038/b209038.txt">Table of n, a(n) for n = 0..1000</a>

%e a(12) = #{12, 9+3, 8+4, 7+5, 6+6, 6+3+3, 5+4+3, 4+4+4, 3+3+3+3} = 9;

%e a(13) = #{13, 10+3, 9+4, 8+5, 7+6, 7+3+3, 6+4+3, 5+5+3, 5+4+4, 4+3+3+3} = 10;

%e a(14) = #{14, 11+3, 10+4, 9+5, 8+6, 8+3+3, 7+7, 7+4+3, 6+5+3, 6+4+4, 5+5+4, 5+3+3+3, 4+4+3+3} = 13;

%e a(15) = #{15, 12+3, 11+4, 10+5, 9+6, 9+3+3, 8+7, 8+4+3, 7+5+3, 7+4+4, 6+6+3, 6+5+4, 6+3+3+3, 5+5+5, 5+4+3+3, 4+4+4+3, 3+3+3+3+3} = 15;

%e a(16) = #{16, 12+4, 11+5, 10+6, 9+7, 8+8, 8+4+4, 7+5+4, 6+6+4, 6+5+5, 4+4+4+4} = 11.

%o (Haskell)

%o a209038 n = p (max 1 (n `div` 4)) n where

%o p _ 0 = 1

%o p k m = if m < k then 0 else p k (m - k) + p (k + 1) m

%Y Cf. A209037, A209039.

%K nonn

%O 0,3

%A _Reinhard Zumkeller_, Mar 04 2012

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 09:28 EDT 2024. Contains 371268 sequences. (Running on oeis4.)