A206417 (5*F(n)+3*L(n)-8)/2.

0, 3, 7, 14, 25, 43, 72, 119, 195, 318, 517, 839, 1360, 2203, 3567, 5774, 9345, 15123, 24472, 39599, 64075, 103678, 167757, 271439, 439200, 710643, 1149847, 1860494, 3010345, 4870843, 7881192, 12752039, 20633235, 33385278, 54018517, 87403799, 141422320

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Feb 07 2012

Keywords

• nonn
• easy

References

• Thomas Koshy, Fibonacci and Lucas Numbers and Applications. Wiley, New York, (2001)

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,-1).

Crossrefs

Cf. A000032, A000045.

Programs

Mathematica

Table[(5*Fibonacci[n] + 3*LucasL[n] - 8)/2, {n, 60}] (* or *) Table[LucasL[n+2] - 4, {n, 60}]

PARI

a(n)=fibonacci(n)+3*fibonacci(n+1)-4 \\ Charles R Greathouse IV, Feb 08 2012

PARI

concat(0, Vec(x^2*(x+3)/((x-1)*(x^2+x-1)) + O(x^100))) \\ Colin Barker, Oct 28 2014

Formula

a(n) = 2*a(n-1)-a(n-3). G.f.: x^2*(x+3) / ((x-1)*(x^2+x-1)). - Colin Barker, Oct 28 2014

Extensions

Name shortened, Joerg Arndt, Oct 28 2014