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Numerators of sequence of fractions defined by a(1) = a(2) = 1; for n > 2, a(n) = (a(n-1)+a(n-2)+1)/a(n-2).
2

%I #7 Oct 04 2012 07:38:40

%S 1,1,3,5,3,9,29,71,751,5095,117707,8786157,1495204807,869159527657,

%T 10563805576326283,3058448407404141530011,

%U 21945047981309619478239602921,78849616271246494204031567399858651677,163732240861295155285004461265839986271194799721161

%N Numerators of sequence of fractions defined by a(1) = a(2) = 1; for n > 2, a(n) = (a(n-1)+a(n-2)+1)/a(n-2).

%e 1, 1, 3, 5, 3, 9/5, 29/15, 71/27, 751/261, 5095/2059, 117707/53321, ...

%p a := 1; b := 1; f := proc(n) option remember; global a,b; if n=1 then RETURN(a); fi; if n=2 then RETURN(b); fi; RETURN((f(n-1)+f(n-2)+1)/f(n-2)); end;

%Y Cf. A076843, A076844.

%K nonn,frac

%O 1,3

%A _N. J. A. Sloane_, Nov 21 2002