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Search: id:A117524
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| A117524 |
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Total number of parts of multiplicity 3 in all partitions of n. |
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+0
2
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| 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
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OFFSET
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1,6
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FORMULA
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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 (deutsch(AT)duke.poly.edu), Apr 29 2006
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EXAMPLE
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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 parantheses)
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MAPLE
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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 (deutsch(AT)duke.poly.edu), Apr 29 2006
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CROSSREFS
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Cf. A024786, A116646.
Adjacent sequences: A117521 A117522 A117523 this_sequence A117525 A117526 A117527
Sequence in context: A143444 A108346 A062761 this_sequence A045683 A080088 A098715
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 26 2006
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