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A006493
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Generalized Lucas numbers.
(Formerly M4063)
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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, 85494900, 155693873, 282551856, 511101624, 921676437, 1657238030, 2971622493, 5314551351
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,3
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REFERENCES
| L. Carlitz and R. Scoville, Zero-one sequences and Fibonacci numbers, Fib. Quart., 15 (1977), 246-254.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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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. has denominator (1-x-x^2)^5.
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MAPLE
| 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..36); # Alois P. Heinz, Aug 26 2008
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CROSSREFS
| Sequence in context: A042419 A037956 A095369 * A037375 A159582 A041553
Adjacent sequences: A006490 A006491 A006492 * A006494 A006495 A006496
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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