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);
PROG
(Python)
from sympy.utilities.iterables import partitions
def A264397(n): return sum(max(p.values()) for p in partitions(n)) # Chai Wah Wu, Sep 17 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Nov 20 2015
STATUS
approved