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A264397 Sum of the sizes of the longest clique of all partitions of n. 2
1, 3, 5, 10, 15, 26, 38, 60, 86, 127, 178, 255, 349, 484, 652, 885, 1174, 1565, 2049, 2689, 3481, 4510, 5779, 7407, 9403, 11933, 15029, 18908, 23636, 29511, 36641, 45432, 56063, 69076, 84753, 103833, 126730, 154438, 187584, 227485, 275056, 332066, 399811 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

a(n) = Sum(k*A091602(n,k), k=1..n).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

G.f.: g(x) = sum(k*(product(1-x^{j*(k+1)}, j>=1) - product(1-x^{j*k}, j>=1)), k>=1)/product(1-x^j, j>=1).

EXAMPLE

a(4) = 10 because the partitions 4,31,22,211,1111 of 4 have longest clique sizes 1,1,2,2,4, respectively.

MAPLE

g := (sum(k*(product(1-x^(j*(k+1)), j = 1 .. 100) - product(1-x^(j*k), j = 1 .. 100)), k = 1 .. 100))/(product(1-x^j, j = 1 .. 100)): gser := series(g, x = 0, 53): seq(coeff(gser, x, n), n = 1 .. 50);

CROSSREFS

Cf. A091602, A243978.

Sequence in context: A126728 A070557 A225751 * A254346 A132302 A308872

Adjacent sequences:  A264394 A264395 A264396 * A264398 A264399 A264400

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Nov 20 2015

STATUS

approved

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Last modified July 22 10:41 EDT 2019. Contains 325219 sequences. (Running on oeis4.)