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 A050613 #13 Jan 05 2025 19:51:36
%S A050613 1,1,3,3,7,7,21,21,47,47,141,141,329,329,987,987,2207,2207,6621,6621,
%T A050613 15449,15449,46347,46347,103729,103729,311187,311187,726103,726103,
%U A050613 2178309,2178309,4870847,4870847,14612541,14612541,34095929,34095929
%N A050613 Products of distinct terms of 1 and rest from A001566: a(n) = Product_{i=0..floor(log_2(n+1))} L(2^i)^bit(n,i).
%C A050613 Used to produce the rows of A050609.
%C A050613 Also Sum(((C(2((n+((n+1) mod 2)) mod (2^floor(log_2(n)))),i) mod 2)*F(n+((n+1) mod 2)-i)),i=0..2((n+((n+1) mod 2)) mod (2^floor(log_2(n))))) or Sum(((C(2((n-(n mod 2)) mod (2^floor(log_2(n)))),i) mod 2)*L(n-(n mod 2)-i)),i=0..2((n-(n mod 2)) mod (2^floor(log_2(n))))) for all n > 1. Here F(n) and L(n) are n-th Fibonacci (A000045) and Lucas (A000032) numbers respectively.
%H A050613 A. Karttunen, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/42-1/quartkarttunen01_2004.pdf">On Pascal's Triangle Modulo 2 in Fibonacci Representation</a>, Fibonacci Quarterly, 42 (2004), 38-46.
%p A050613 with(combinat); A050613 := n -> product('luc(2^i)^bit_i(n,i)','i'=0..floor_log_2(n+1));
%p A050613 luc := n -> (fibonacci(n-1)+fibonacci(n+1));
%p A050613 bit_i := (n,i) -> `mod`(floor(n/(2^i)),2);
%p A050613 floor_log_2 := proc(n) local nn,i; nn := n; for i from -1 to n do if(0 = nn) then RETURN(i); fi; nn := floor(nn/2); od; end;
%Y A050613 Bisection: A050614.
%K A050613 nonn
%O A050613 0,3
%A A050613 _Antti Karttunen_, Dec 02 1999