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!)
A184639 Number of partitions of n having no parts with multiplicity 4. 8

%I #12 Apr 30 2018 12:24:47

%S 1,1,2,3,4,7,10,14,19,27,37,50,67,88,115,153,196,253,324,412,524,661,

%T 828,1036,1290,1603,1980,2443,2997,3671,4487,5460,6631,8034,9703,

%U 11703,14075,16890,20226,24175,28838,34332,40801,48394,57307,67765,79974

%N Number of partitions of n having no parts with multiplicity 4.

%H Alois P. Heinz, <a href="/A184639/b184639.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = A000041(n) - A183561(n).

%F a(n) = A183568(n,0) - A183568(n,4).

%F G.f.: Product_{j>0} (1-x^(4*j)+x^(5*j))/(1-x^j).

%e a(4) = 4, because 4 partitions of 4 have no parts with multiplicity 4: [1,1,2], [2,2], [1,3], [4].

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

%p add((l->`if`(j=4, [l[1]$2], l))(b(n-i*j, i-1)), j=0..n/i)))

%p end:

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

%p seq(a(n), n=0..50);

%t b[n_, i_] := b[n, i] = If[n == 0, {1, 0}, If[i<1, {0, 0}, Sum[Function[l, If[j == 4, {l[[1]], l[[1]]}, l]][b[n - i*j, i - 1]], {j, 0, n/i}]]];

%t a[n_] := b[n, n][[1]] - b[n, n][[2]];

%t Table[a[n], {n, 0, 50}] (* _Jean-François Alcover_, Apr 30 2018, after _Alois P. Heinz_ *)

%Y Cf. A000041, A183561, A183568, A007690, A116645, A118807, A184640, A184641, A184642, A184643, A184644, A184645.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Jan 18 2011

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 28 07:48 EDT 2024. Contains 371235 sequences. (Running on oeis4.)