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A117524
Total number of parts of multiplicity 3 in all partitions of n.
4
0, 0, 1, 0, 1, 2, 3, 3, 7, 8, 13, 17, 25, 32, 48, 59, 83, 108, 145, 183, 247, 310, 406, 512, 659, 824, 1055, 1307, 1651, 2047, 2558, 3146, 3913, 4788, 5904, 7202, 8821, 10707, 13054, 15770, 19118, 23027, 27775, 33312, 40029, 47835, 57231, 68182, 81261
OFFSET
1,6
LINKS
FORMULA
G.f. for total number of parts of multiplicity m in all partitions of n is (x^m/(1-x^m)-x^(m+1)/(1-x^(m+1)))/Product(1-x^i,i=1..infinity).
a(n) = Sum(k*A118806(n,k), k>=0). - Emeric Deutsch, Apr 29 2006
a(n) ~ exp(Pi*sqrt(2*n/3)) / (24*Pi*sqrt(2*n)). - Vaclav Kotesovec, May 24 2018
EXAMPLE
a(9) = 7 because among the 30 (=A000041(9)) partitions of 9 only [6,(1,1,1)],[4,2,(1,1,1)],[(3,3,3)],[3,3,(1,1,1)],[3,(2,2,2)],[(2,2,2),(1,1,1)] contain parts of multiplicity 3 and their total number is 7 (shown between parentheses)
MAPLE
g:=(x^3/(1-x^3)-x^4/(1-x^4))/product(1-x^i, i=1..65): gser:=series(g, x=0, 62): seq(coeff(gser, x, n), n=1..58); # Emeric Deutsch, Apr 29 2006
CROSSREFS
Cf. A024786, A116646. Column k=3 of A197126.
Sequence in context: A335050 A062761 A375515 * A308513 A045683 A343031
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Apr 26 2006
STATUS
approved