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!)
A184640 Number of partitions of n having no parts with multiplicity 5. 8
1, 1, 2, 3, 5, 6, 11, 14, 21, 28, 39, 51, 72, 92, 124, 160, 210, 266, 349, 438, 562, 704, 892, 1107, 1395, 1720, 2141, 2631, 3249, 3965, 4873, 5916, 7216, 8730, 10585, 12742, 15387, 18443, 22151, 26466, 31646, 37659, 44873, 53212, 63149, 74666, 88295 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = A000041(n) - A183562(n).

a(n) = A183568(n,0) - A183568(n,5).

G.f.: Product_{j>0} (1-x^(5*j)+x^(6*j))/(1-x^j).

EXAMPLE

a(5) = 6, because 6 partitions of 5 have no parts with multiplicity 5: [1,1,1,2], [1,2,2], [1,1,3], [2,3], [1,4], [5].

MAPLE

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

      add((l->`if`(j=5, [l[1]$2], l))(b(n-i*j, i-1)), j=0..n/i)))

    end:

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

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

MATHEMATICA

b[n_, i_] := b[n, i] = If[n == 0, {1, 0}, If[i < 1, {0, 0}, Sum[Function[l, If[j == 5, {l[[1]], l[[1]]}, l]][b[n - i*j, i - 1]], {j, 0, n/i}]]];

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

Table[a[n], {n, 0, 50}] (* Jean-Fran├žois Alcover, Apr 30 2018, after Alois P. Heinz *)

CROSSREFS

Cf. A000041, A183562, A183568, A007690, A116645, A118807, A184639, A184641, A184642, A184643, A184644, A184645.

Sequence in context: A050049 A132581 A238542 * A240490 A039839 A039844

Adjacent sequences:  A184637 A184638 A184639 * A184641 A184642 A184643

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jan 18 2011

STATUS

approved

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 May 21 06:36 EDT 2022. Contains 353889 sequences. (Running on oeis4.)