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A206776
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a(n) = 3*a(n-1) + 2*a(n-2) for n>1, a(0)=2, a(1)=3.
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2
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2, 3, 13, 45, 161, 573, 2041, 7269, 25889, 92205, 328393, 1169589, 4165553, 14835837, 52838617, 188187525, 670239809, 2387094477, 8501763049, 30279478101, 107841960401, 384084837405, 1367938433017, 4871984973861, 17351831787617, 61799465310573
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OFFSET
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0,1
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COMMENTS
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This is the Lucas sequence V(3,-2).
Inverse binomial transform of this sequence is A072265.
Is a(n)+1 = A124805(n) for n>0?
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LINKS
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Bruno Berselli, Table of n, a(n) for n = 0..200
Wikipedia, Lucas sequence: Specific names.
Index to sequences with linear recurrences with constant coefficients, signature (3,2).
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FORMULA
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G.f.: (2-3*x)/(1-3*x-2*x^2).
a(n) = ((3-sqrt(17))^n+(3+sqrt(17))^n)/2^n.
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MATHEMATICA
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RecurrenceTable[{a[n] == 3 a[n - 1] + 2 a[n - 2], a[0] == 2, a[1] == 3}, a[n], {n, 25}]
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PROG
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(MAGMA) [n le 1 select n+2 else 3*Self(n)+2*Self(n-1): n in [0..25]];
(Maxima) a[0]:2$ a[1]:3$ a[n]:=3*a[n-1]+2*a[n-2]$ makelist(a[n], n, 0, 25);
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CROSSREFS
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Cf. A189736 (same recurrence but with initial values reversed).
Sequence in context: A122719 A106866 A164133 * A214888 A203985 A164511
Adjacent sequences: A206773 A206774 A206775 * A206777 A206778 A206779
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KEYWORD
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nonn,easy
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AUTHOR
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Bruno Berselli, Jan 10 2013
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STATUS
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approved
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