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Search: id:A055979
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| A055979 |
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Solutions (value of r) of Diophantine equation 2*x^2 + 3*x + 2 = r^2. |
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+0
2
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| 4, 11, 134, 373, 4552, 12671, 154634, 430441, 5253004, 14622323, 178447502, 496728541, 6061962064, 16874148071, 205928262674, 573224305873, 6995498968852, 19472752251611, 237641036678294, 661500352248901
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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A necessary condition on any solution of the equation is x = [r/sqrt(2)] where [] denotes the floor function. The problem is connected to Bresenham's circle rendering algorithm. The sequence lists the radii of circles where the algorithm creates an undesired 90-degree cusp at x = y.
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FORMULA
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a(n) = A006452(2n+3) if n=0, 2, 4, ... a(n) = A006452(2n+2) if n=1, 3, 5, ...
G.f.: (4+11*x-2*x^2-x^3) / (1+x^4-34*x^2). [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jun 03 2009]
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MAPLE
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a:= n-> (Matrix([11, 4, 1, 2]). Matrix([[0, 1, 0, 0], [34, 0, 1, 0], [0, 0, 0, 1], [ -1, 0, 0, 0]])^n)[1, 2]: seq (a(n), n=0..25); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jun 03 2009]
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CROSSREFS
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Cf. A006452.
Sequence in context: A004796 A125888 A167418 this_sequence A018242 A006248 A119571
Adjacent sequences: A055976 A055977 A055978 this_sequence A055980 A055981 A055982
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KEYWORD
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nonn,nice
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AUTHOR
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Helge Robitzsch (hrobi(AT)math.uni-goettingen.de), Jul 24 2000
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EXTENSIONS
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More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jun 03 2009
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