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 A383609 #10 May 03 2025 04:08:09
%S A383609 1,1,1,1,2,1,1,3,4,1,1,4,8,8,1,1,5,13,20,17,1,1,6,19,38,50,38,1,1,7,
%T A383609 26,63,107,126,89,1,1,8,34,96,196,296,322,216,1,1,9,43,138,326,588,
%U A383609 814,834,539,1,1,10,53,190,507,1052,1728,2236,2187,1374,1
%N A383609 Triangle read by rows: T(n,k) = T(n-1, k-2) + T(n-1, k-1) + T(n-1, k) for 0 < k < n, T(n,0) = T(n,n) = 1.
%F A383609 Sum_{k=0..n} 2^(n-k)*(T(n, k)(mod 2)) = A038185(n).
%F A383609 Sum_{j=0..n}(Sum_{k=0..j} T(j, k)) = A211278(n).
%F A383609 T(n,k) = A167630(n,n-k).
%e A383609 Triangle T(n, k) starts:
%e A383609 n\k : 0 1 2 3 4 5 6 7
%e A383609 ====================================================================
%e A383609 0 : 1
%e A383609 1 : 1 1
%e A383609 2 : 1 2 1
%e A383609 3 : 1 3 4 1
%e A383609 4 : 1 4 8 8 1
%e A383609 5 : 1 5 13 20 17 1
%e A383609 6 : 1 6 19 38 50 38 1
%e A383609 7 : 1 7 26 63 107 126 89 1
%e A383609 ...
%p A383609 T := proc (n, k) option remember; if k = n or k = 0 then 1 elif k < 0 then 0 else T(n-1, k-2)+T(n-1, k-1)+T(n-1, k) end if end proc:
%p A383609 seq(print(seq(T(n, k), k = 0 .. n)), n = 0 .. 8);
%Y A383609 Cf. A038185, A167630, A211278.
%K A383609 nonn,tabl
%O A383609 0,5
%A A383609 _Mélika Tebni_, May 02 2025