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 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

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