login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A320375 Number of parts in all partitions of n with largest multiplicity five. 2

%I

%S 5,0,6,6,13,18,34,35,66,82,120,154,230,286,408,514,699,886,1189,1485,

%T 1949,2441,3136,3906,4980,6159,7757,9555,11908,14600,18062,22000,

%U 27028,32804,39996,48327,58614,70489,85036,101876,122284,145943,174419,207354,246804

%N Number of parts in all partitions of n with largest multiplicity five.

%H Alois P. Heinz, <a href="/A320375/b320375.txt">Table of n, a(n) for n = 5..1000</a>

%F a(n) ~ log(6) * exp(Pi*sqrt(5*n)/3) / (2 * Pi * 5^(1/4) * n^(1/4)). - _Vaclav Kotesovec_, Oct 25 2018

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

%p add((l->l+[0, l[1]*j])(b(n-i*j, i-1, k)), j=0..min(n/i, k))))

%p end:

%p a:= n-> (k-> (b(n$2, k)-b(n$2, k-1))[2])(5):

%p seq(a(n), n=5..50);

%t b[n_, i_, k_] := b[n, i, k] = If[n == 0, {1, 0}, If[i < 1, {0, 0}, Sum[Function[l, {0, l[[1]] j} + l][b[n - i j, i - 1, k]], {j, 0, Min[n/i, k]}]]];

%t a[n_] := With[{k = 5}, (b[n, n, k] - b[n, n, k - 1])[[2]]];

%t a /@ Range[5, 50] (* _Jean-Fran├žois Alcover_, Dec 13 2020, after _Alois P. Heinz_ *)

%Y Column k=5 of A213177.

%K nonn

%O 5,1

%A _Alois P. Heinz_, Oct 11 2018

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 18 08:27 EDT 2021. Contains 348067 sequences. (Running on oeis4.)