710647

Appears in sequences

• Lucas numbers (beginning with 1): L(n) = L(n-1) + L(n-2) with L(1) = 1, L(2) = 3.at n=27A000204
• a(n) = 3*a(n-2) - a(n-4), a(0)=2, a(1)=1, a(2)=3, a(3)=2. Alternates Lucas (A000032) and Fibonacci (A000045) sequences for even and odd n.at n=28A005247
• Bisection of Lucas numbers: a(n) = L(2*n) = A000032(2*n).at n=14A005248
• Odd Lucas numbers.at n=18A014447
• Number of maximum matchings in the n-Moebius ladder M_n.at n=28A020878
• Numerators of continued fraction convergents to sqrt(45).at n=13A041076
• Numerators of continued fraction convergents to sqrt(845).at n=5A042630
• a(n) = 4*a(n-1) + a(n-2); a(0)=1, a(1)=7.at n=9A048876
• Shifts left two places under BIN1 transform.at n=28A052341
• a(n) = Lucas(4*n).at n=7A056854
• Fibonacci-type sequence based on subtraction: a(0) = 1, a(1) = 2 and a(n) = a(n-2) - a(n-1).at n=29A061084
• a(n) = floor(tau^n) + 1, where tau = (1 + sqrt(5))/2.at n=28A062724
• a(n) = gcd(1 + Fibonacci(n+1), 1 + Fibonacci(n)).at n=57A063726
• Sum of Lucas numbers and inverted Lucas numbers: a(n) = A000032(n)*A075193(n).at n=26A075270
• log_phi(n) is closer to an integer than is log_phi(m) for any m with 2<=m<n, where phi=(1+sqrt(5))/2 is the golden ratio.at n=27A080023
• a(n) = Lucas(7*n).at n=4A087281
• a(n) = gcd(Lucas(n)+1, Fibonacci(n)+1).at n=56A115313
• Lucas numbers for which the product of the digits is a Fibonacci number.at n=9A117769
• G.f.: x^2*(3+3*x-2*x^2)/ ( (x^2-x-1) * (x^2+x-1)).at n=27A122012
• a(n) = (F(2*n-1) + F(2*n+1))*(5/6 - cos(2*Pi*n/3)/3), where F(n) = Fibonacci(n).at n=14A128052