Define the Fibonacci polynomials by F[1] = 1, F[2] = x; for n > 2, F[n] = x*F[n-1] + F[n-2] (cf. A049310, A053119). Swamy's inequality states that F[n]^2 <= G[n] = (x^2 + 1)^2*(x^2 + 2)^(n-3) for all n >= 3 and all real x. The sequence gives a triangle of the coefficients of the even exponents of G[n] - F[n]^2 read by rows.
A335444
Define the Fibonacci polynomials by F[1] = 1, F[2] = x; for n > 2, F[n] = x*F[n-1] + F[n-2] (cf. A049310, A053119). Swamy's inequality states that F[n]^2 <= G[n] = (x^2 + 1)^2*(x^2 + 2)^(n-3) for all n >= 3 and all real x. The sequence gives a triangle of the coefficients of the even exponents of G[n] - F[n]^2 read by rows.
Terms
- a(0) =0a(1) =2a(2) =1a(3) =3a(4) =6a(5) =2a(6) =8a(7) =19a(8) =14a(9) =3a(10) =15a(11) =52a(12) =58a(13) =26a(14) =4a(15) =32a(16) =128a(17) =192a(18) =132a(19) =42a(20) =5a(21) =63a(22) =300a(23) =558a(24) =518a(25) =253a(26) =62a(27) =6a(28) =128a(29) =679
External references
- oeis: A335444