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A049666
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F(5n)/5, where F=A000045 (the Fibonacci sequence).
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19
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0, 1, 11, 122, 1353, 15005, 166408, 1845493, 20466831, 226980634, 2517253805, 27916772489, 309601751184, 3433536035513, 38078498141827, 422297015595610, 4683345669693537, 51939099382224517, 576013438874163224
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 12 2010: (Start)
For more information about this type of recurrence follow the Khovanova link and see A054413, A086902 and A178765.
(End)
For n >=2, a(n) equals the permanent of the (n-1)X(n-1) tridiagonal matrix with 11's along the main diagonal and 1's along the subdiagonal and the superdiagonal. [From John M. Campbell, Jul 08 2011]
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LINKS
| Tanya Khovanova, Recursive Sequences
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FORMULA
| G.f.: x/(1-11*x-x^2).
a(n)=11a(n-1)+a(n-2) for n>1, a(0)=0, a(1)=1. With a=golden ratio and b=1-a, a(n)=(a^(5n)-b^(5n))/(5*Sqrt(5)). - Mario Catalani (mario.catalani(AT)unito.it), Jul 24 2003
a(n)=F(n, 11), the n-th Fibonacci polynomial evaluated at x=11. - T. D. Noe (noe(AT)sspectra.com), Jan 19 2006
a(n)=((11+sqrt(125))^n-(11-sqrt(125))^n)/(2^n*sqrt(125)). [From Al Hakanson (hawkuu(AT)gmail.com), Jan 12 2009]
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 12 2010: (Start)
a(2n) = 11*A049670(n), a(2n+1) = A097843(n).
a(3n+1) = A041227(5n), a(3n+2) = A041227(5n+3), a(3n+3) = 2*A041227(5n+4).
Limit(a(n+k)/a(k), k=infinity) = (A001946(n) + A049666(n)*sqrt(125))/2.
Limit(A001946(n)/A049666(n), n=infinity) = sqrt(125).
(End)
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MATHEMATICA
| Table[Fibonacci[5*n]/5, {n, 0, 100}] (T. D. Noe, Oct 29 2009)
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PROG
| (Mupad) numlib::fibonacci(5*n)/5 $ n = 0..25; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2008
sage: from sage.combinat.sloane_functions import recur_gen3 sage: it = recur_gen3(0, 1, 11, 11, 1, 0) sage: [it.next() for i in xrange(1, 22)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 09 2008
(Other) sage: [lucas_number1(n, 11, -1) for n in xrange(0, 19)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 27 2009]
(Other) sage: [fibonacci(5*n)/5 for n in xrange(0, 19)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 15 2009]
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CROSSREFS
| A column of array A028412.
A102312 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 15 2009]
Sequence in context: A110398 A176595 A067218 * A163462 A041222 A097708
Adjacent sequences: A049663 A049664 A049665 * A049667 A049668 A049669
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jan 20 2000
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