0,3

a(n) / a(n-1) converges to 5^1/2 + 1 as n approaches infinity. 5^1/2 + 1 can also be written as Phi^3 - 1, 2 * Phi, Phi^2 + Phi - 1 and (L(n) / F(n)) + 1, where L(n) is the n-th Lucas number and F(n) is the n-th Fibonacci number as n approaches infinity.

Binomial transform is A001076. - Paul Barry (pbarry(AT)wit.ie), Aug 25 2003

Eric Weisstein, Horadam Sequence

Eric Weisstein, Fibonacci Number

Eric Weisstein, Pell Number

Eric Weisstein, Lucas Number

Eric Weisstein, Lucas Sequence

a(n) = s*a(n-1) + r*a(n-2); for n > 1, where a(0) = 0, a(1) = 1, s = 2, r = 4

G.f.: x/(1-2x-4x^2); a(n)=sqrt(5)((1+sqrt(5))^n-(1-sqrt(5))^n)/10; a(n)=sum{k=0..floor(n/2), C(n, 2k+1)5^k }. - Paul Barry (pbarry(AT)wit.ie), Aug 25 2003

The signed version 0, 1, -2, ... has a(n)=sqrt(5)((sqrt(5)-1)^n-(-sqrt(5)-1)^n)/10. It is the second inverse binomial transform of A085449. - Paul Barry (pbarry(AT)wit.ie), Aug 25 2003

a(n)=2^(n-1)Fib(n). - Paul Barry (pbarry(AT)wit.ie), Mar 22 2004

a(4) = 24 because a(3) = 8, a(2) = 2, s = 2, r = 4 and (2 * 8) + (4 * 2) = 24.

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*(a[n-1]+2*a[n-2]) od: seq(a[n], n=0..26); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 17 2008

Cf. A024318, A000032, A000129, A001076, A085939.

Essentially the same as A063727.

Sequence in context: A093833 A006952 A034741 this_sequence A063727 A127362 A133443

Adjacent sequences: A085446 A085447 A085448 this_sequence A085450 A085451 A085452

easy,nonn

Ross La Haye (rlahaye(AT)new.rr.com), Aug 18 2003