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Search: id:A127002
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| A127002 |
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Number of partitions of n that have the form a+a+b+c where a,b,c are distinct. |
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1
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| 0, 0, 0, 0, 0, 0, 1, 2, 4, 3, 7, 8, 11, 11, 17, 17, 23, 23, 30, 31, 39, 38, 48, 49, 58, 58, 70, 70, 82, 82, 95, 96, 110, 109, 125, 126, 141, 141, 159, 159, 177, 177, 196, 197, 217, 216, 238, 239, 260, 260, 284, 284, 308, 308, 333, 334, 360, 359, 387, 388, 415, 415, 445
(list; graph; listen)
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OFFSET
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1,8
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FORMULA
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G.f.: (3*x^2+2*x+1)*x^7/(1-x^4)/(1-x^3)/(1-x^2). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jan 03 2007
G.f.=Sum(Sum(Sum(x^(i+j+k)*(x^i+x^j+x^k),i=1..j-1),j=2..k-1),k=3..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 05 2007
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EXAMPLE
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a(10) counts these partitions: {1,1,2,6}, (1,1,3,5), {2,2,1,5}.
a(11) counts {1,1,2,7}, {1,1,3,6}, {1,1,4,5}, {2,2,1,6}, {2,2,3,4}, {3,3,1,4}, {4,4,1,2}
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MAPLE
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g:=sum(sum(sum(x^(i+j+k)*(x^i+x^j+x^k), i=1..j-1), j=2..k-1), k=3..80): gser:=series(g, x=0, 70): seq(coeff(gser, x, n), n=1..65); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 05 2007
isA127002 := proc(p) local s; if nops(p) = 4 then s := convert(p, set) ; if nops(s) = 3 then RETURN(1) ; else RETURN(0) ; fi ; else RETURN(0) ; fi ; end: A127002 := proc(n) local part, res, p; part := combinat[partition](n) ; res := 0 ; for p from 1 to nops(part) do res := res+isA127002(op(p, part)) ; od ; RETURN(res) ; end: for n from 1 to 200 do print(A127002(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 07 2007
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CROSSREFS
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Cf. A000041.
Sequence in context: A021808 A105081 A026167 this_sequence A027634 A101267 A090568
Adjacent sequences: A126999 A127000 A127001 this_sequence A127003 A127004 A127005
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Jan 01 2007
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