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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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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; refs; listen; history; internal format)
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OFFSET
| 0,4
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REFERENCES
| N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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
| 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
| 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
| 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
| Sequence in context: A076593 A129774 A049373 * A068981 A099631 A199396
Adjacent sequences: A002533 A002534 A002535 * A002537 A002538 A002539
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Better description and more terms from David W. Wilson (davidwwilson(AT)comcast.net) Aug 15 1996.
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