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%I #7 Sep 10 2016 15:14:06
%S 1,1,2,3,4,6,9,13,19,29,43,65,97,146,219,328,493,739,1108,1663,2494,
%T 3741,5611,8417,12626,18938,28408,42611,63917,95876,143813,215720,
%U 323580,485370,728055,1092082,1638123,2457185,3685777,5528666,8292999
%N Floor((x^n - (1-x)^n)/2 +.5) where x = (sqrt(4)+1)/2 = 3/2.
%C This is analogous to the closed form of the formula for the n-th Fibonacci number. Even before truncation, these numbers are rational and the decimal part always ends in 5. For x=(sqrt(4)+1)/2=3/2, a(n)/a(n-1) -> x.
%F The general form of x is (sqrt(r)+1)/2, r=1,2,3..
%F a(n) = floor(b(n)/2^n) where b(n) = 2^(n-1)+A152011(n). - _R. J. Mathar_, Sep 10 2016
%o (PARI) g(n,r) = for(m=1,n,print1(fib(m,r)",")) fib(n,r) = x=(sqrt(r)+1)/2;floor((x^n-(1-x)^n)/sqrt(r)+.5)
%K nonn
%O 1,3
%A _Cino Hilliard_, Apr 01 2008