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

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A319818 Number of partitions of n into exactly eight positive triangular numbers. 5

%I #4 Sep 28 2018 11:19:35

%S 1,0,1,0,1,1,1,1,1,2,2,2,2,2,4,3,4,3,4,5,6,4,6,6,7,7,7,8,9,11,9,10,11,

%T 11,14,13,13,15,16,15,18,18,18,19,22,20,22,25,23,27,26,26,29,29,32,32,

%U 36,31,37,39,37,39,42,41,47,48,44,48,52,52,54,55,55

%N Number of partitions of n into exactly eight positive triangular numbers.

%H Alois P. Heinz, <a href="/A319818/b319818.txt">Table of n, a(n) for n = 8..10000</a>

%F a(n) = [x^n y^8] 1/Product_{j>=1} (1-y*x^A000217(j)).

%p h:= proc(n) option remember; `if`(n<1, 0,

%p `if`(issqr(8*n+1), n, h(n-1)))

%p end:

%p b:= proc(n, i, k) option remember; `if`(n=0, `if`(k=0, 1, 0), `if`(

%p k>n or i*k<n, 0, b(n, h(i-1), k)+b(n-i, h(min(n-i, i)), k-1)))

%p end:

%p a:= n-> b(n, h(n), 8):

%p seq(a(n), n=8..120);

%Y Column k=8 of A319797.

%Y Cf. A000217.

%K nonn

%O 8,10

%A _Alois P. Heinz_, Sep 28 2018

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.

Last modified December 10 18:13 EST 2023. Contains 367717 sequences. (Running on oeis4.)