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Search: id:A131576
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| A131576 |
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Number of ways to represent n as sum of even number of consecutive integers. |
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+0
1
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| 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 2, 1, 1, 0, 1, 1, 2, 0, 1, 1, 1, 0, 2, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 1, 2, 0, 2, 1, 1, 1, 1, 1, 2, 0, 2, 1, 1, 1, 2, 1, 1, 0, 1, 1, 3, 1, 1, 2, 1, 0, 2, 1, 1, 1, 2, 1, 2, 0, 1, 2, 1, 1, 2, 1, 2, 0, 1, 1, 2, 1, 1, 2, 1, 0, 4
(list; graph; listen)
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OFFSET
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1,21
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COMMENT
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Number of odd divisors of n greater than sqrt(2*n).
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FORMULA
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G.f.: Sum_{k>1} x^(k*(2*k+1))/(1-x^(2*k)).
a(A000040(i))=1 for i=1,2,3,... a(A000079(j))=0 for j=0,1,2,3,... - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 13 2007
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EXAMPLE
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a(11)=1 because we have 11=5+6; a(21)=2 because we have 21=10+11=1+2+3+4+5+6; a(75)=3 because we have 75=37+38=10+11+12+13+14+15=3+4+5+6+7+8+9+10+11+12.
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MAPLE
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G:=sum(x^(k*(2*k+1))/(1-x^(2*k)), k=1..10): Gser:=series(G, x=0, 85): seq(coeff(Gser, x, n), n=1..80); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Sep 08 2007
A131576 := proc(n) local dvs, a, k, r; dvs := numtheory[divisors](n) ; a := 0 ; for k in dvs do r := n/k+1 ; if r mod 2 = 0 then if r/2-k >= 1 then a := a+1 ; fi ; fi ; od: RETURN(a) ; end: seq(A131576(n), n=1..120) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 13 2007
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CROSSREFS
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Cf. A082647, A001227.
Sequence in context: A037870 A026920 A060763 this_sequence A100073 A075685 A037906
Adjacent sequences: A131573 A131574 A131575 this_sequence A131577 A131578 A131579
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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), Aug 28 2007, Sep 16 2007
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