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A033891
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Fibonacci(4n+3).
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12
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2, 13, 89, 610, 4181, 28657, 196418, 1346269, 9227465, 63245986, 433494437, 2971215073, 20365011074, 139583862445, 956722026041, 6557470319842, 44945570212853, 308061521170129, 2111485077978050
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (7,-1).
Tanya Khovanova, Recursive Sequences
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FORMULA
| a(n) = 7*a(n-1)-a(n-2). - Floor van Lamoen (fvlamoen(AT)hotmail.com), Dec 10 2001
a(n) = (7/2-(3/2)*sqrt(5))^n-(2/5)*(7/2-(3/2)*sqrt(5))^n*sqrt(5)+(2/5)*sqrt(5)*(7/2+(3/2) *sqrt(5))^n+(7/2+(3/2)*sqrt(5))^n, with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 25 2008
G.f.: (2-x)/(1-7*x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 17 2008]
a(n) = Fibonacci(2*n+2)^2 + Fibonacci(2*n+1)^2. [From Gary Detlefs, Oct 12 2011]
a(n) = 2*A004187(n+1)-A004187(n). - R. J. Mathar, Nov 26 2011
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MATHEMATICA
| Table[Fibonacci[4*n+3], {n, 0, 14}] (Vladimir Orlovsky, Jul 21 2008)
LinearRecurrence[{7, -1}, {2, 13}, 31] (* or *) CoefficientList[Series[ (2-x)/(1-7x+x^2), {x, 0, 30}], x] (* From Harvey P. Dale, May 03 2011 *)
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PROG
| (MAGMA) [Fibonacci(4*n +3): n in [0..100]]; // Vincenzo Librandi, Apr 17 2011
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CROSSREFS
| a(n) = A167816(4*n+3). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 13 2009]
Sequence in context: A092849 A106938 A106937 * A172968 A126035 A074617
Adjacent sequences: A033888 A033889 A033890 * A033892 A033893 A033894
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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