

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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,6


LINKS

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


FORMULA

G.f. for total number of parts of multiplicity m in all partitions of n is (x^m/(1x^m)x^(m+1)/(1x^(m+1)))/Product(1x^i,i=1..infinity).
a(n) = Sum(k*A118806(n,k), k>=0).  Emeric Deutsch, Apr 29 2006


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/(1x^3)x^4/(1x^4))/product(1x^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: A222294 A181850 A062761 * A045683 A157531 A155755
Adjacent sequences: A117521 A117522 A117523 * A117525 A117526 A117527


KEYWORD

easy,nonn


AUTHOR

Vladeta Jovovic, Apr 26 2006


STATUS

approved



