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2, 4, 8, 18, 42, 100, 240, 578, 1394, 3364, 8120, 19602, 47322, 114244, 275808, 665858, 1607522, 3880900, 9369320, 22619538, 54608394, 131836324, 318281040, 768398402, 1855077842, 4478554084, 10812186008, 26102926098, 63018038202, 152139002500, 367296043200, 886731088898, 2140758220994, 5168247530884
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refs;
listen;
history;
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internal format)
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OFFSET
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0,1
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COMMENTS
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a(n) = A078057(n) + 1 (see A288213). - Michel Dekking, Sep 29 2019
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..1000
J. V. Leyendekkers and A. G. Shannon, Pellian sequence relationships among pi, e, sqrt(2), Notes on Number Theory and Discrete Mathematics, Vol. 18, 2012, No. 2, 58-62. See Table 2.
Index entries for linear recurrences with constant coefficients, signature (3,-1,-1).
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FORMULA
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From Colin Barker, May 26 2018: (Start)
G.f.: 2*(1 - x - x^2) / ((1 - x)*(1 - 2*x - x^2)).
a(n) = (2 + (1-sqrt(2))^(1+n) + (1+sqrt(2))^(1+n)) / 2.
a(n) = 3*a(n-1) - a(n-2) - a(n-3) for n>2.
(End)
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PROG
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(PARI) Vec(2*(1 - x - x^2) / ((1 - x)*(1 - 2*x - x^2)) + O(x^40)) \\ Colin Barker, May 26 2018
(MAGMA) a:=[2, 4, 8]; [n le 3 select a[n] else 3*Self(n-1) - Self(n-2) - Self(n-3):n in [1..35]]; // Marius A. Burtea, Sep 29 2019
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CROSSREFS
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Cf. A024537.
Sequence in context: A306200 A057151 A026699 * A078678 A261492 A027056
Adjacent sequences: A182777 A182778 A182779 * A182781 A182782 A182783
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Dec 23 2012
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STATUS
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approved
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