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 A136424 #11 Jul 28 2021 06:59:02 %S A136424 1,1,2,4,6,11,19,32,55,95,164,283,488,842,1451,2503,4318,7447,12844, %T A136424 22152,38207,65898,113657,196029,338101,583137,1005763,1734685, %U A136424 2991888,5160244,8900104,15350410,26475540,45663552,78757977,135837417 %N A136424 a(n) = floor((x^n - (1-x)^n) / (2x-1) +.5) where x = (sqrt(6)+1)/2 (and hence 2x-1 = sqrt(6)). %C A136424 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(6)+1)/2, a(n)/a(n-1) -> x. %F A136424 The general form of x is (sqrt(r)+1)/2, r=1,2,3.. %F A136424 a(n) = floor(b(n)/2^n) where b(n) = 2*A002532(n)+2^(n-1). - _R. J. Mathar_, Sep 10 2016 %o A136424 (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 A136424 nonn %O A136424 1,3 %A A136424 _Cino Hilliard_, Apr 01 2008 %E A136424 Definition corrected by Frederic van der Plancke (fplancke(AT)hotmail.com), May 08 2009