A179134 a(n) = (F(2*n-1) + F(2*n+2)) * (5/6 - cos(2*Pi*n/3)/3), where F(n) = Fibonacci(n).

1, 4, 10, 13, 68, 178, 233, 1220, 3194, 4181, 21892, 57314, 75025, 392836, 1028458, 1346269, 7049156, 18454930, 24157817, 126491972, 331160282, 433494437, 2269806340, 5942430146, 7778742049, 40730022148, 106632582346

Offset: 0

Author

Johannes W. Meijer, Jul 01 2010

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,18,0,0,-1).

Crossrefs

Cf. A128052, A000045 (Fibonacci numbers).

Appears in A179133.

Programs

Maple

with(combinat): nmax:=28; for n from 0 to nmax do a(n):=(fibonacci(2*n-1)+fibonacci(2*n+2))*(5/6-cos(2*Pi*n/3)/3) od: seq(a(n),n=0..nmax);

Formula

a(n) = 18*a(n-3)-a(n-6). G.f.: -(2*x^5+4*x^4+5*x^3-10*x^2-4*x-1) / ((x^2-3*x+1)*(x^4+3*x^3+8*x^2+3*x+1)). - Colin Barker, Jun 27 2013