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A033891
a(n) = Fibonacci(4*n+3).
19
2, 13, 89, 610, 4181, 28657, 196418, 1346269, 9227465, 63245986, 433494437, 2971215073, 20365011074, 139583862445, 956722026041, 6557470319842, 44945570212853, 308061521170129, 2111485077978050
OFFSET
0,1
FORMULA
a(n) = 7*a(n-1) - a(n-2). - Floor van Lamoen, Dec 10 2001
G.f.: (2-x)/(1-7*x+x^2). - Philippe Deléham, Nov 17 2008
a(n) = A167816(4*n+3). - Reinhard Zumkeller, Nov 13 2009
a(n) = Fibonacci(2*n+2)^2 + Fibonacci(2*n+1)^2. - Gary Detlefs, Oct 12 2011
a(n) = 2*A004187(n+1) - A004187(n). - R. J. Mathar, Nov 26 2011
a(n) = A004187(n+1) + A049685(n). - Yuriy Sibirmovsky, Sep 15 2016
From Peter Bala, Aug 11 2022: (Start)
Let n ** m = n*m + floor(phi*n)*floor(phi*m), where phi = (1 + sqrt(5))/2, denote the Porta-Stolarsky star product of the integers n and m (see A101858). Then a(n) = 2 ** 2 ** ... ** 2 (n+1 factors).
a(2*n+1) = a(n) ** a(n) = Fibonacci(8*n+7); a(3*n+2) = a(n) ** a(n) ** a(n) = Fibonacci(12*n+11) and so on. (End)
MATHEMATICA
Table[Fibonacci[4*n+3], {n, 0, 30}] (* Vladimir Joseph Stephan Orlovsky, Jul 21 2008 *)
LinearRecurrence[{7, -1}, {2, 13}, 31] (* or *) CoefficientList[Series[ (2-x)/(1-7x+x^2), {x, 0, 30}], x] (* Harvey P. Dale, May 03 2011 *)
PROG
(Magma) [Fibonacci(4*n+3): n in [0..30]]; // Vincenzo Librandi, Apr 17 2011
(PARI) a(n)=fibonacci(4*n+3) \\ Charles R Greathouse IV, Sep 24 2015
(Sage) [fibonacci(4*n+3) for n in (0..30)] # G. C. Greubel, Jul 14 2019
(GAP) List([0..30], n-> Fibonacci(4*n+3)); # G. C. Greubel, Jul 14 2019
CROSSREFS
KEYWORD
nonn,easy
STATUS
approved