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A183567 Number of partitions of n containing a clique of size 10. 12
1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 13, 15, 22, 26, 37, 45, 61, 74, 99, 120, 157, 192, 247, 299, 381, 462, 580, 703, 874, 1055, 1303, 1569, 1921, 2309, 2808, 3363, 4070, 4859, 5848, 6964, 8342, 9903, 11817, 13988, 16623, 19626, 23240, 27363, 32297 (list; graph; refs; listen; history; text; internal format)
OFFSET

10,5

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 = 10..1000

FORMULA

G.f.: (1-Product_{j>0} (1-x^(10*j)+x^(11*j))) / (Product_{j>0} (1-x^j)).

EXAMPLE

a(14) = 2, because 2 partitions of 14 contain (at least) one clique of size 10: [1,1,1,1,1,1,1,1,1,1,2,2], [1,1,1,1,1,1,1,1,1,1,4].

MAPLE

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

      add((l->`if`(j=10, [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=10..60);

MATHEMATICA

max = 60; f = (1 - Product[1 - x^(10j) + x^(11j), {j, 1, max}])/Product[1 - x^j, {j, 1, max}]; s = Series[f, {x, 0, max}]; Drop[CoefficientList[s, x], 10] (* Jean-Fran├žois Alcover, Oct 01 2014 *)

CROSSREFS

10th column of A183568. Cf. A000041, A183558, A183559, A183560, A183561, A183562, A183563, A183564, A183565, A183566.

Sequence in context: A026929 A206560 A035554 * A222710 A032278 A222738

Adjacent sequences:  A183564 A183565 A183566 * A183568 A183569 A183570

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jan 05 2011

STATUS

approved

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Last modified January 24 16:34 EST 2020. Contains 331207 sequences. (Running on oeis4.)