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Search: id:A006493
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| A006493 |
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Generalized Lucas numbers.
(Formerly M4063)
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+0
2
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| 1, 0, 6, 7, 28, 54, 135, 286, 627, 1313, 2730, 5565, 11212, 22304, 43911, 85614, 165490, 317373, 604296, 1143054, 2149074, 4017950, 7473180, 13832910, 25490115, 46774448
(list; graph; listen)
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OFFSET
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3,3
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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).
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.
L. Carlitz and R. Scoville, Zero-one sequences and Fibonacci numbers, Fib. Quart., 15 (1977), 246-254.
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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. has denominator (1-x-x^2)^5.
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MAPLE
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A006493:=(1-2*z+2*z**2)*(z-1)**3/(z**2+z-1)**5; [Conjectured by S. Plouffe in his 1992 dissertation.]
a:= n-> (Matrix([[7, 6, 0, 1, 0$4, -2, 18]]). Matrix(10, (i, j)-> if (i=j-1) then 1 elif j=1 then [5, -5, -10, 15, 11, -15, -10, 5, 5, 1][i] else 0 fi)^n)[1, 7]: seq (a(n), n=3..28); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 26 2008]
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CROSSREFS
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Sequence in context: A042419 A037956 A095369 this_sequence A037375 A159582 A041553
Adjacent sequences: A006490 A006491 A006492 this_sequence A006494 A006495 A006496
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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