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Search: id:A002536
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| A002536 |
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a(n) = 8 a(n-2) - 9 a(n-4).
(Formerly M3783 N1540)
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+0
2
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| 0, 1, 1, 5, 8, 31, 55, 203, 368, 1345, 2449, 8933, 16280, 59359, 108199, 394475, 719072, 2621569, 4778785, 17422277, 31758632, 115784095, 211059991, 769472267, 1402652240, 5113721281, 9321678001, 33984519845, 61949553848, 225852667231
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
A. Tarn, Approximations to certain square roots and the series of numbers connected therewith, Mathematical Questions and Solutions from the Educational Times, 1 (1916), 8-12.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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G.f.= x(1+x-3x^2)/(1-8x^2+9x^4). A002537(n)/a(n) converges to sqrt(7). - Mario Catalani (mario.catalani(AT)unito.it), Apr 24 2003
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MAPLE
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A002536:=-z*(-1-z+3*z**2)/(1-8*z**2+9*z**4); [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Sequence in context: A076593 A129774 A049373 this_sequence A068981 A099631 A032790
Adjacent sequences: A002533 A002534 A002535 this_sequence A002537 A002538 A002539
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Better description and more terms from David W. Wilson (davidwwilson(AT)comcast.net) Aug 15 1996.
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