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 A362379 #11 Apr 20 2023 11:31:35
%S A362379 1,0,1,2,0,1,1,4,0,1,5,2,6,0,1,5,14,3,8,0,1,14,14,27,4,10,0,1,19,49,
%T A362379 27,44,5,12,0,1,42,68,113,44,65,6,14,0,1,66,175,159,214,65,90,7,16,0,
%U A362379 1,131,286,465,304,360,90,119,8,18,0,1
%N A362379 Convolution triangle of A052547(n).
%F A362379 T(n,k) = T(n-1,k) + T(n-1,k-1) + 2*T(n-2,k) - T(n-2,k-1) - T(n-3,k) ; T(0,0) = T(1,1) = T(2,2) = 1, T(1,0) = T(2,1) = 0, T(2,0) = 2, T(n,k) = 0 if k<0 or if k>n .
%F A362379 Sum_{k = 0..n} T(n,k)*x^k = A052547(n), A077998(n), A052536(n), A052941(n) for x = 0, 1, 2, 3 respectively.
%F A362379 Sum_{k = 0..n} T(n,k)*2^(n-k) = A139818(n+1) = A001045(n+1)^2.
%e A362379 Triangle begins, for n>=0, 0<=k<=n :
%e A362379 1 ;
%e A362379 0, 1 ;
%e A362379 2, 0, 1 ;
%e A362379 1, 4, 0, 1 ;
%e A362379 5, 2, 6, 0, 1 ;
%e A362379 5, 14, 3, 8, 0, 1 ;
%e A362379 14, 14, 27, 4, 10, 0, 1 ;
%e A362379 19, 49, 27, 44, 5, 12, 0, 1 ;
%e A362379 42, 68, 113, 44, 65, 6, 14, 0, 1 ;
%e A362379 ...
%Y A362379 Cf. A052547, A077998 (row sums), A052964 (diagonal sums).
%K A362379 nonn,easy,tabl
%O A362379 0,4
%A A362379 _Philippe Deléham_, Apr 20 2023