id:A057105 - OEIS Search Results

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Triangle of numbers (when unsigned) related to congruum problem: T(n,k)=k^2+2nk-n^2 with n>k>0 and starting at T(2,1)=1.

+0
2

1, -2, 7, -7, 4, 17, -14, -1, 14, 31, -23, -8, 9, 28, 49, -34, -17, 2, 23, 46, 71, -47, -28, -7, 16, 41, 68, 97, -62, -41, -18, 7, 34, 63, 94, 127, -79, -56, -31, -4, 25, 56, 89, 124, 161, -98, -73, -46, -17, 14, 47, 82, 119, 158, 199, -119, -92, -63, -32, 1, 36, 73, 112, 153, 196, 241, -142, -113, -82, -49, -14, 23, 62, 103 (list; table; graph; listen)

	OFFSET	`1,2`
	COMMENT	`Signed values are only relevant for the explicit formula.`
	LINKS	`Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.`
	FORMULA	`Unsigned: a(n) =sqrt(A055096(n)^2-A057103(n)) =sqrt(A056203(n)^2-2*A057103(n)).`
	EXAMPLE	`a(1)=T(2,1)=1^2+221-2^2=1`
	CROSSREFS	`Cf. A057102. The congruum problem is about finding solutions for h (A057103) where there are integers x (A055096), y (A057105 unsigned) and z (A056203) such that h=x^2-y^2=z^2-x^2.` `Sequence in context: A020770 A164767 A021977 this_sequence A016536 A063503 A068386` `Adjacent sequences: A057102 A057103 A057104 this_sequence A057106 A057107 A057108`
	KEYWORD	`sign,tabl`
	AUTHOR	`Henry Bottomley (se16(AT)btinternet.com), Aug 02 2000`

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Last modified March 20 09:10 EDT 2010. Contains 173642 sequences.

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