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A015524
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a(n) = 3*a(n-1) + 7*a(n-2).
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16
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0, 1, 3, 16, 69, 319, 1440, 6553, 29739, 135088, 613437, 2785927, 12651840, 57457009, 260933907, 1185000784, 5381539701, 24439624591, 110989651680, 504046327177, 2289066543291, 10395523920112, 47210037563373
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Linear 2nd order recurrence.
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FORMULA
| O.g.f.: -x/(-1+3*x+7*x^2). a(n)=14^n*(1/A^n -(-1)^n/B^n)/sqrt(37) where A=sqrt(37)-3 = A010491-3 and B = sqrt(37)+3=A010491+3 - R. J. Mathar, Apr 21 2008.
a(n) = (7*(111+23*sqrt(37))*(1/2*(3+sqrt(37)))^n+(2553+431*sqrt(37))*(1/2 (3-sqrt(37)))^n)/(518*(45+8*sqrt(37))) [From Harvey P. Dale, Jul 4 2011]
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MATHEMATICA
| a[n_]:=(MatrixPower[{{1, 3}, {1, -4}}, n].{{1}, {1}})[[2, 1]]; Table[Abs[a[n]], {n, -1, 40}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 19 2010]
LinearRecurrence[{3, 7}, {0, 1}, 30] (* From Harvey P. Dale, July 04 2011 *)
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PROG
| (Sage) [lucas_number1(n, 3, -7) for n in xrange(0, 23)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
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CROSSREFS
| Sequence in context: A044046 A179600 A000269 * A012279 A037098 A038602
Adjacent sequences: A015521 A015522 A015523 * A015525 A015526 A015527
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KEYWORD
| nonn,easy
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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