STATUS
proposed
approved
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Revision History for A059502
(Bold, blue-underlined text is an addition; faded, red-underlined text is anewer changes | Showing entries 11-20 | older changes
a(n) = (3*n*F(2n-1) + (3-n)*F(2n))/5 where F() = Fibonacci numbers A000045.
(history; published version)
(history; published version)
STATUS
editing
proposed
FORMULA
G.f.= : x(1-x)(1-2x)/(1-3x+x^2)^2. - Emeric Deutsch, Oct 07 2002
a(n) = A147703(n,1). - Philippe Deléham, Nov 29 2008
STATUS
proposed
editing
STATUS
editing
proposed
NAME
a(n) = (3*n*F(2n-1) + (3-n)*F(2n))/5 where F() = Fibonacci numbers A000045.
LINKS
Harry J. Smith, <a href="/A059502/b059502.txt">Table of n, a(n) for n = 0,...,200</a>
FORMULA
a(n)=A147703(n,1). [From _- _Philippe Deléham_, Nov 29 2008]
EXAMPLE
1 3 9 27 80 ...
2 5 14 40 ...
3 7 19 ...
4 9 5 ...
PROG
(PARI) { for (n = 0, 200, write("b059502.txt", n, " ", (3*n*fibonacci(2*n - 1) + (3 - n)*fibonacci(2*n))/5); ) } [From _\\ _Harry J. Smith_, Jun 27 2009]
(MAGMA) [(3*n*Fibonacci(2*n-1)+(3-n)*Fibonacci(2*n))/5: n in [0..100]]; // _Vincenzo Librandi, _, Apr 23 2011
STATUS
approved
editing
LINKS
<a href="/index/Rec#order_04">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (6,-11,6,-1).
AUTHOR
_Floor van Lamoen (fvlamoen(AT)hotmail.com), _, Jan 19 2001
MATHEMATICA
Table[(3n Fibonacci[2n-1]+(3-n)Fibonacci[2n])/5, {n, 0, 30}] (* or *) CoefficientList[Series[x(1-x)(1-2x)/(1-3x+x^2)^2, {x, 0, 30}], x] (* From _Harvey P. Dale, _, Apr 23 2011 *)
FORMULA
a(n)=A147703(n,1). [From _Philippe DELEHAM_, Deléham_, Nov 29 2008]
STATUS
editing
approved