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%I #7 Jan 16 2022 01:25:41
%S 1,1,3,4,8,14,25,46,84,153,279,509,927,1691,3082,5618,10241,18667,
%T 34028,62029,113070,206113,375719,684889,1248467,2275800,4148501,
%U 7562201,13784953,25128255,45805684,83498067,152206593,277453693,505763582
%N a(n) = floor((x^n-(1-x)^n)/sqrt(7)+1/2) where x = (sqrt(7)+1)/2.
%C This is analogous to 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(7)+1)/2, a(n)/a(n-1) -> x. The general form of x is (sqrt(r)+1)/2, r=1,2,3..
%F Asymptotically a(n) ~ A083099(n)/2^(n-1). - _R. J. Mathar_, Apr 20 2008
%F a(n) = floor(b(n)/2^n) where b(n) = 2*A083099(n)+2^(n-1). - _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
%E Definition corrected by _R. J. Mathar_, Apr 20 2008
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