1860498

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=29A000204
• a(n) = 11*a(n-1) + a(n-2).at n=6A001946
• 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=30A005247
• Bisection of Lucas numbers: a(n) = L(2*n) = A000032(2*n).at n=15A005248
• a(n) = L(L(n+1)+1), where L(n) are Lucas numbers A000032.at n=6A005372
• Even Lucas numbers: a(n) = L(3*n).at n=10A014448
• Number of maximum matchings in the n-Moebius ladder M_n.at n=30A020878
• Numerators of continued fraction convergents to sqrt(320).at n=9A041604
• Fibonacci-type sequence based on subtraction: a(0) = 1, a(1) = 2 and a(n) = a(n-2) - a(n-1).at n=31A061084
• a(n) = floor(tau^n) + 1, where tau = (1 + sqrt(5))/2.at n=30A062724
• a(n) = gcd(1 + Fibonacci(n+1), 1 + Fibonacci(n)).at n=61A063726
• a(n) = Lucas(10*n).at n=3A065705
• Sum of Lucas numbers and inverted Lucas numbers: a(n) = A000032(n)*A075193(n).at n=28A075270
• 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=29A080023
• Lucas(6*n): a(n) = 18*a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 18.at n=5A087215
• a(n) = L(P(n)), where P = A000041 (partition numbers) and L = A000032 (Lucas numbers).at n=9A100845
• a(n) = gcd(Lucas(n)-1, Fibonacci(n)+1).at n=58A115312
• Lucas numbers for which the product of the digits is a Fibonacci number.at n=10A117769
• G.f.: x^2*(3+3*x-2*x^2)/ ( (x^2-x-1) * (x^2+x-1)).at n=29A122012
• a(n) = A014217(n+1) - A115360(n+2).at n=28A142584