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Search: id:A001584
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| A001584 |
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A generalized Fibonacci sequence.
(Formerly M0235 N0080)
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+0
1
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| 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 4, 4, 4, 7, 7, 8, 12, 12, 16, 21, 21, 31, 37, 38, 58, 65, 71, 106, 114, 135, 191, 201, 257, 341, 359, 485, 605, 652, 904, 1070, 1202, 1664, 1894, 2237, 3029, 3370, 4176, 5464, 6048, 7779, 9793, 10963, 14411, 17492, 20054, 26507, 31239, 36924, 48396
(list; graph; listen)
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OFFSET
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0,9
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REFERENCES
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V. C. Harris, Generalized Fibonacci sequences associated with a generalized Pascal triangle, Fib. Quart., 4 (1966), 241-248.
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).
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
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.: (1+x+x^2-x^3-x^4-x^5)/(1-2*x^3+x^6-x^8).
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MAPLE
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A001584:=(z-1)*(z**2+z+1)**2/(z**4-z**3+1)/(z**4+z**3-1); [S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Cf. A017817.
Sequence in context: A029047 A007294 A053282 this_sequence A112801 A089873 A096323
Adjacent sequences: A001581 A001582 A001583 this_sequence A001585 A001586 A001587
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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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More terms from David W. Wilson (davidwwilson(AT)comcast.net)
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