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 A357298 #58 Jan 11 2023 06:41:08 %S A357298 0,1,1,0,1,0,1,1,1,1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,1,1,1,1,1, %T A357298 1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1, %U A357298 1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 %N A357298 Triangle read by rows where all entries in every even row are 1's and the entries in every odd row alternate between 0 (start/end) and 1. %C A357298 Row sums are equal to n for even n and (n-1)/2 for odd n; or A065423(n+1). %F A357298 T(n, k) = 1/2 + (1/2)*(-1)^(n*(k+1)), for n >= 1 and 0 <= k <= n-1. %F A357298 T(n, k) = (2^n - 2^(n-k-1) - 2^k) mod 3, for n >= 1 and 0 <= k <= n-1. %F A357298 T(n, k) = A358125(n, k) mod 3, for n >= 1 and 0 <= k <= n-1. %e A357298 Triangle begins: %e A357298 n\k 0 1 2 3 4 5 6 7 8 9 ... %e A357298 1 0; %e A357298 2 1, 1; %e A357298 3 0, 1, 0; %e A357298 4 1, 1, 1, 1; %e A357298 5 0, 1, 0, 1, 0; %e A357298 6 1, 1, 1, 1, 1, 1; %e A357298 7 0, 1, 0, 1, 0, 1, 0; %e A357298 8 1, 1, 1, 1, 1, 1, 1, 1; %e A357298 9 0, 1, 0, 1, 0, 1, 0, 1, 0; %e A357298 10 1, 1, 1, 1, 1, 1, 1, 1, 1, 1; %e A357298 ... %e A357298 Formatted as a symmetric triangle -- regular hexagram pattern with 0's at the centers formed by connecting all 1's: %e A357298 .----------------------------------------------. %e A357298 | k=0 1 2 3 4 5 | %e A357298 |-----------------------/---/---/---/---/--./ | %e A357298 ------- / / / / / | %e A357298 | n=1 | 0 / / / / /| | %e A357298 ------- / / / / | 6 | %e A357298 | 2 | 1---1 / / / / |/ | %e A357298 ------- \ / / / / / | %e A357298 | 3 | 0 1 0 / / / /| | %e A357298 ------- / \ / / / | 7 | %e A357298 | 4 | 1---1---1---1 / / / |/ | %e A357298 ------- \ / \ / / / / | %e A357298 | 5 | 0 1 0 1 0 / / /| | %e A357298 ------- / \ / \ / / | 8 | %e A357298 | 6 | 1---1---1---1---1---1 / / |/ | %e A357298 ------- \ / \ / \ / / / | %e A357298 | 7 | 0 1 0 1 0 1 0 / /| | %e A357298 ------- / \ / \ / \ / | 9 | %e A357298 | 8 | 1---1---1---1---1---1---1---1 / / | %e A357298 ------- \ / \ / \ / \ / / | %e A357298 | 9 | 0 1 0 1 0 1 0 1 0 /| | %e A357298 ------- / \ / \ / \ / \ | . | %e A357298 | 10 | 1---1---1---1---1---1---1---1---1---1 | . | %e A357298 ------- | . | %p A357298 T := n -> local k; seq(1/2 + 1/2*(-1)^(n*(k + 1)), k = 0 .. n - 1); # formula 1 %p A357298 seq(T(n), n=1..16); # print first 16 rows of formula 1. %o A357298 (PARI) T(n,k) = bitnegimply(1,n) || bitand(1,k); \\ _Kevin Ryde_, Dec 21 2022 %Y A357298 Cf. A358125, A065423 (row sums). %K A357298 nonn,easy,tabl %O A357298 1,1 %A A357298 _Ambrosio Valencia-Romero_, Dec 20 2022