4870846

Appears in sequences

• a(n) = a(n-1) + a(n-2) + 1, with a(0) = 0 and a(1) = 2.at n=31A001610
• a(n) = F(2n+1) + F(2n-1) - 1.at n=16A005592
• Number of cyclic binary n-bit strings with no alternating substring of length > 2.at n=31A007039
• Number of (marked) cyclic n-bit binary strings containing no runs of length > 2.at n=31A007040
• a(n) = floor(phi^n), where phi = (1+sqrt(5))/2 is the golden ratio.at n=32A014217
• Cyclotomic polynomials Phi_n at x=phi, ceiled up (where phi = tau = (sqrt(5)+1)/2).at n=31A063707
• a(n) = Fibonacci(n-1) + Fibonacci(n+1) - (-1)^n.at n=32A098600
• a(n) = L(3*n)/L(n), where L(n) = Lucas number.at n=16A110391
• a(n) = A014217(n+1) - A115360(n+2).at n=30A142584
• a(n+1) = a(n)^2 + 2*a(n) - 2 and a(1) = 2.at n=4A145502
• a(n+1) = a(n)^2 + 2*a(n) - 2 and a(1) = 6.at n=3A145506
• Terms in A014217 pairwise swapped.at n=33A154699
• Continued fraction expansion for exp( Sum_{n>=1} 1/(n*Lucas(n)) ), where Lucas(n) = A000032(n) = ((1+sqrt(5))/2)^n + ((1-sqrt(5))/2)^n.at n=45A174505
• a(n) = a(n-1) + a(n-2) + (-1)^n, with a(0)=0 and a(1)=1.at n=33A181716
• Subsequence of A014217 (n=2,3,5,6,8,9,11,12,...).at n=20A182642
• a(0) = a(1) = a(2) = a(3) = 1; for n > 3, a(n) = (a(n-1)^2+a(n-2)^2+a(n-3)^2+a(n-1)+a(n-2)+a(n-3))/a(n-4).at n=7A276271
• Number of nonempty subsets of {1, ..., n} containing no two cyclically successive elements.at n=32A324015
• a(n) = (-1)^n * A000032(n) - 1.at n=32A355021