id:A055112 - OEIS Search Results

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Consider Pythagorean triangles (X,Y,Z=Y+1=X^2+Y^2). Sequence gives areas.

+0
4

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; listen)

	OFFSET	`0,2`
	FORMULA	`a(n) = n(n+1)(2n+1) = 6A000330(n) = A007531(2n)/4 = 3A000292(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`
	CROSSREFS	`X values A005408, Y values A046092, Z values A001844, perimeter A002939 (offset)..` `Cf. A033581.` `Sequence in context: A050972 A002444 A152788 this_sequence A094143 A009775 A119536` `Adjacent sequences: A055109 A055110 A055111 this_sequence A055113 A055114 A055115`
	KEYWORD	`nonn`
	AUTHOR	`Henry Bottomley (se16(AT)btinternet.com), Jun 15 2000`

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Last modified November 27 14:34 EST 2009. Contains 167570 sequences.

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