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 A181175 #4 Jun 02 2025 03:12:58 %S A181175 1,2,40,320,21504,688128,178257920,22817013760,23433341566976, %T A181175 11997870882291712,49179307930885816320,100719222642454151823360, %U A181175 1650485975228872480767606784,13520781109074923362448234774528 %N A181175 The "Fi1" sums of the powers-of-2 triangle A000079. %C A181175 The a(n) represent the Fi1(n) sums, see A180662, of the powers-of-2 triangle A000079. We observe that Fi2(2*n) = Fi1(2*n) and Fi2(2*n+1) = 2*Fi1(2*n+1). %F A181175 a(2*n+1) = 2^(2*n+1)*a(2*n) and a(2*n+2) = 2^(2*n+2)*((4^(n+2) - 1)/(4^(n+1) - 1))*a(2*n+1) with a(0) = 1 and a(1) =2. %p A181175 nmax:=13: a(0):=1: a(1):=2: for n from 0 to nmax/2 do a(2*n+1):= 2^(2*n+1)*a(2*n): a(2*n+2):=2^(2*n+2)*((4^(n+2) - 1)/(4^(n+1) - 1))*a(2*n+1): od: seq(a(n),n=0..nmax); %K A181175 easy,nonn %O A181175 0,2 %A A181175 _Johannes W. Meijer_, Oct 10 2010