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

 

Logo

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 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A183563 Number of partitions of n containing a clique of size 6. 13
1, 0, 1, 1, 2, 2, 5, 5, 8, 10, 15, 18, 27, 33, 47, 57, 78, 96, 129, 159, 208, 258, 330, 407, 517, 635, 798, 978, 1217, 1482, 1833, 2225, 2729, 3303, 4028, 4856, 5885, 7070, 8528, 10211, 12259, 14628, 17494, 20800, 24777, 29378, 34867 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,5

COMMENTS

All parts of a number partition with the same value form a clique. The size of a clique is the number of elements in the clique.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 6..1000

FORMULA

G.f.: (1-Product_{j>0} (1-x^(6*j)+x^(7*j))) / (Product_{j>0} (1-x^j)).

EXAMPLE

a(10) = 2, because 2 partitions of 10 contain (at least) one clique of size 6: [1,1,1,1,1,1,2,2], [1,1,1,1,1,1,4].

MAPLE

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

      add((l->`if`(j=6, [l[1]$2], l))(b(n-i*j, i-1)), j=0..n/i)))

    end:

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

seq(a(n), n=6..55);

MATHEMATICA

max = 55; f = (1 - Product[1 - x^(6j) + x^(7j), {j, 1, max}])/Product[1 - x^j, {j, 1, max}]; s = Series[f, {x, 0, max}]; Drop[CoefficientList[s, x], 6] (* Jean-François Alcover, Oct 01 2014 *)

CROSSREFS

6th column of A183568. Cf. A000041, A183558, A183559, A183560, A183561, A183562, A183564, A183565, A183566, A183567.

Sequence in context: A238945 A340572 A091609 * A222706 A240495 A304393

Adjacent sequences:  A183560 A183561 A183562 * A183564 A183565 A183566

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jan 05 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 07:55 EST 2021. Contains 349571 sequences. (Running on oeis4.)