OFFSET
0,1
COMMENTS
For n>0, a(n) is the area of the trapezoid defined by the four points (F(n+1), F(n+2)), (F(n+2), F(n+1)), (F(n+3), F(n+4)), and (F(n+4), F(n+3)) where F(n) = A000045(n). - J. M. Bergot, May 14 2014
REFERENCES
Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,-8,1).
FORMULA
a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3).
G.f.: (4-17*x+3*x^2)/((1-x)*(1-7*x+x^2)). - Colin Barker, Jun 22 2012
MAPLE
with(combinat) for n from 0 to 30 do printf(`%d, `, fibonacci(4*n+3)+2) od # James A. Sellers, Mar 03 2003
MATHEMATICA
Table[Fibonacci[4n+3] +2, {n, 0, 30}] (* or *)
Table[Fibonacci[2n+3]*LucasL[2n], {n, 0, 30}] (* Alonso del Arte, Apr 18 2011 *)
LinearRecurrence[{8, -8, 1}, {4, 15, 91}, 30] (* Harvey P. Dale, Apr 22 2017 *)
PROG
(Magma) [Fibonacci(4*n+3)+2: n in [0..30]]; // Vincenzo Librandi, Apr 18 2011
(PARI) vector(30, n, n--; fibonacci(4*n+3)+2) \\ G. C. Greubel, Jul 14 2019
(Sage) [fibonacci(4*n+3)+2 for n in (0..30)] # G. C. Greubel, Jul 14 2019
(GAP) List([0..30], n-> Fibonacci(4*n+3) -2); # G. C. Greubel, Jul 14 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. K. Guy, Mar 01 2003
EXTENSIONS
More terms from James A. Sellers, Mar 03 2003
STATUS
approved