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 A050609 #12 Jan 05 2025 19:51:36
%S A050609 0,1,1,3,3,1,12,6,4,2,21,21,9,7,3,77,35,33,15,11,5,168,126,56,54,24,
%T A050609 18,8,609,273,203,91,87,39,29,13,987,987,441,329,147,141,63,47,21,
%U A050609 3572,1598,1596,714,532,238,228,102,76,34,7755,5781,2585,2583,1155,861,385
%N A050609 Table T(n,k) = Sum_{i=0..2n} (C(2n,i) mod 2)*F(i+k) = Sum_{i=0..n} (C(n,i) mod 2)*F(2i+k).
%C A050609 Listed antidiagonalwise as T(0,0), T(1,0), T(0,1), T(2,0), T(1,1), T(0,2), ...
%H A050609 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.
%F A050609 Also a(n) = A075148(n, k)*A050613(n).
%p A050609 A050609_as_sum := proc(n,k) local i; RETURN(add(((binomial(n,i) mod 2)*fibonacci(k+2*i)),i=0..n)); end;
%p A050609 A050609_as_product := (n,k) -> (`if`(1 = (n mod 2),luc(n+k),fibonacci(n+k)))*product('luc(2^i)^bit_i(n,i)','i'=1..floor_log_2(n+1)); # Produces same answers.
%p A050609 [seq(A050609_as_sum(A025581(n), A002262(n)),n=0..119)];
%Y A050609 Transpose of A050610. First row: A051656, second row: A050611, third row: A048757, fourth row: A050612. A050613 gives other Maple procedures. Cf. A025581, A002262.
%K A050609 nonn,tabl
%O A050609 0,4
%A A050609 _Antti Karttunen_, Dec 02 1999