This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A136425 #7 Jan 16 2022 01:25:41 %S A136425 1,1,3,4,8,14,25,46,84,153,279,509,927,1691,3082,5618,10241,18667, %T A136425 34028,62029,113070,206113,375719,684889,1248467,2275800,4148501, %U A136425 7562201,13784953,25128255,45805684,83498067,152206593,277453693,505763582 %N A136425 a(n) = floor((x^n-(1-x)^n)/sqrt(7)+1/2) where x = (sqrt(7)+1)/2. %C A136425 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 A136425 Asymptotically a(n) ~ A083099(n)/2^(n-1). - _R. J. Mathar_, Apr 20 2008 %F A136425 a(n) = floor(b(n)/2^n) where b(n) = 2*A083099(n)+2^(n-1). - _R. J. Mathar_, Sep 10 2016 %o A136425 (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 A136425 nonn %O A136425 1,3 %A A136425 _Cino Hilliard_, Apr 01 2008 %E A136425 Definition corrected by _R. J. Mathar_, Apr 20 2008