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A081011 a(n) = Fibonacci(4n+3) + 2, or Fibonacci(2n+3)*Lucas(2n). 1
4, 15, 91, 612, 4183, 28659, 196420, 1346271, 9227467, 63245988, 433494439, 2971215075, 20365011076, 139583862447, 956722026043, 6557470319844, 44945570212855, 308061521170131, 2111485077978052, 14472334024676223 (list; graph; refs; listen; history; text; internal format)
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).

a(n) = 2 + [(7/2)-(3/2)*sqrt(5)]^n + [(7/2)+(3/2)*sqrt(5)]^n + (2/5)*sqrt(5)*{[(7/2) + (3/2)*sqrt(5))^n - [(7/2)-(3/2)*sqrt(5)]^n}, with n >= 0. - Paolo P. Lava, Dec 01 2008

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

Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers).

Sequence in context: A306178 A304920 A076900 * A008829 A322920 A013193

Adjacent sequences:  A081008 A081009 A081010 * A081012 A081013 A081014

KEYWORD

nonn,easy

AUTHOR

R. K. Guy, Mar 01 2003

EXTENSIONS

More terms from James A. Sellers, Mar 03 2003

STATUS

approved

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Last modified November 21 14:18 EST 2019. Contains 329371 sequences. (Running on oeis4.)