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A055112
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Consider Pythagorean triangles (X,Y,Z=Y+1=X^2+Y^2). Sequence gives areas.
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6
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0, 6, 30, 84, 180, 330, 546, 840, 1224, 1710, 2310, 3036, 3900, 4914, 6090, 7440, 8976, 10710, 12654, 14820, 17220, 19866, 22770, 25944, 29400, 33150, 37206, 41580, 46284, 51330, 56730, 62496, 68640, 75174, 82110, 89460, 97236, 105450
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) is the set of possible y values for 4x^3+x^2=y^2 with the x values being A002378(n) [From Gary Detlefs (gdetlefs(AT)aol.com), Feb 22 2010]
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FORMULA
| a(n) = n(n+1)(2n+1) = 6*A000330(n) = A007531(2n)/4 = 3*A000292(2n-1)/2 = A005408(n)*A046092(n)/2 = A005408(n)*(A001844(n)-1)/2
Sum(n>0, 1/a(n))=3-4ln(2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 30 2002
a(n) = SUM[i=1..n] 6*i^2 = SUM[i=1..n] A033581(i). - Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 15 2006
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MATHEMATICA
| f[n_]:=n(n+1)(2n+1); Table[f[n], {n, 0, 5!}] [From Vladimir Joseph Stephan Orlovsky (4vladimir(AT)gmail.com), 21 Nov 2010]
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CROSSREFS
| X values A005408, Y values A046092, Z values A001844, perimeter A002939 (offset)..
Cf. A033581.
Sequence in context: A050972 A002444 A152788 * A094143 A009775 A119536
Adjacent sequences: A055109 A055110 A055111 * A055113 A055114 A055115
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KEYWORD
| nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jun 15 2000
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