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Search: id:A162330
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| A162330 |
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Blocks of 4 numbers of the form 2k, 2k-1, 2k, 2k+1, k=1,2,3,4,... |
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+0
1
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| 2, 1, 2, 3, 4, 3, 4, 5, 6, 5, 6, 7, 8, 7, 8, 9, 10, 9, 10, 11, 12, 11, 12, 13, 14, 13, 14, 15, 16, 15, 16, 17, 18, 17, 18, 19, 20, 19, 20, 21, 22, 21, 22, 23, 24, 23, 24, 25, 26, 25, 26, 27, 28, 27, 28, 29, 30, 29, 30, 31, 32, 31, 32, 33, 34, 33, 34, 35, 36, 35, 36, 37, 38, 37
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This illustrates the infinite product Pi/2 = product_{k=1..infinity} ((2*k)/(2k-1))*((2k)/(2k+1)).
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LINKS
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Eric W. Weisstein, Wallis Formula MathWorld
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FORMULA
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a(n) = a(n-1)+a(n-4)-a(n-5). G.f.: x*(2-x+x^2+x^3-x^4)/((1+x) * (1+x^2) * (x-1)^2 ).
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CROSSREFS
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Cf. A000796, A019669.
Sequence in context: A076258 A030330 A059261 this_sequence A134967 A084612 A030339
Adjacent sequences: A162327 A162328 A162329 this_sequence A162331 A162332 A162333
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KEYWORD
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nonn,easy
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AUTHOR
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Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jul 01 2009
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EXTENSIONS
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Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 16 2009
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