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Search: id:A162155
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| A162155 |
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Integer quartets a(4k)= 2, a(4k+1) = 32*k^2-24*k+3, a(4k+2) = 32*k^2-24*k+2, a(4k+3) = 8*k-3, k>=1. |
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+0
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| 2, 11, 10, 5, 2, 83, 82, 13, 2, 219, 218, 21, 2, 419, 418, 29, 2, 683, 682, 37, 2, 1011, 1010, 45, 2, 1403, 1402, 53, 2, 1859, 1858, 61, 2, 2379, 2378, 69, 2, 2963, 2962, 77, 2, 3611, 3610, 85, 2, 4323, 4322, 93, 2, 5099, 5098, 101, 2, 5939, 5938, 109, 2, 6843, 6842, 117
(list; graph; listen)
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OFFSET
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4,1
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COMMENT
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The members of each quartet are interrelated by the Diophantine formula,
( (4*k-3)^2+(4*k-2)^2 ) * ( (4*k-1)^2+(4*k)^2 ) = a(4*k)^2 + a(4*k+1)^2 = a(4*k+2)^2 + a(4*k+3)^2 .
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FORMULA
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a(n)= a(n-1) -a(n-2) +a(n-3) +2*a(n-4) -2*a(n-5) +2*a(n-6) -2*a(n-7) -a(n-8) +a(n-9) -a(n-10) +a(n-11).
G.f.: x^4* (-2-9*x-x^2-4*x^3+8*x^4-58*x^5+6*x^6+2*x^8-5*x^9+3*x^10-4*x^7)/( (1+x)^2 * (x-1)^3 * (x^2+1)^3 ).
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EXAMPLE
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k=1 contributes the quartet (2,11,10,5). k=2 contributes (2,83,82,13) etc.
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CROSSREFS
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Cf. A000027.
Sequence in context: A009204 A023642 A025536 this_sequence A163344 A064743 A109868
Adjacent sequences: A162152 A162153 A162154 this_sequence A162156 A162157 A162158
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KEYWORD
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nonn,less
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AUTHOR
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Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jun 26 2009
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EXTENSIONS
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Edited and corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 04 2009
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