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 A304223 #25 Sep 05 2018 02:29:11 %S A304223 1,1,1,-2,1,-4,2,1,-6,8,1,-8,18,-8,1,-10,32,-32,4,1,-12,50,-80,36,1, %T A304223 -14,72,-160,136,-24,1,-16,98,-280,360,-160,8,1,-18,128,-448,780,-592, %U A304223 128,1,-20,162,-672,1484,-1632,720,-64 %N A304223 Triangle read by rows: T(0,0)=1; T(n,k) = T(n-1,k)-2*T(n-2,k-1)+2*T(n-3,k-2) for k = 0..floor(2*n/3); T(n,k)=0 for n or k < 0. %C A304223 The numbers in rows of the triangle are along skew diagonals pointing top-left in center-justified triangle given in A304209. %C A304223 The coefficients in the expansion of 1/(1-x+2*x^2-2*x^3) are given by the sequence generated by the row sums. %D A304223 Shara Lalo and Zagros Lalo, Polynomial Expansion Theorems and Number Triangles, Zana Publishing, 2018, ISBN: 978-1-9995914-0-3, pp. 204, 205. %H A304223 Shara Lalo, <a href="/A304223/a304223.pdf">Left-justified Triangle</a> %e A304223 Triangle begins: %e A304223 1; %e A304223 1; %e A304223 1, -2; %e A304223 1, -4, 2; %e A304223 1, -6, 8; %e A304223 1, -8, 18, -8; %e A304223 1, -10, 32, -32, 4; %e A304223 1, -12, 50, -80, 36; %e A304223 1, -14, 72, -160, 136, -24; %e A304223 1, -16, 98, -280, 360, -160, 8; %e A304223 1, -18, 128, -448, 780, -592, 128; %e A304223 1, -20, 162, -672, 1484, -1632, 720, -64; %e A304223 1, -22, 200, -960, 2576, -3752, 2624, -640, 16; %e A304223 ... %o A304223 (PARI) T(n,k) = if ((n<0) || (k<0), 0, if ((n==0) && (k==0), 1, T(n-1,k)-2*T(n-2,k-1)+2*T(n-3,k-2))); %o A304223 tabf(nn) = for (n=0, nn, for (k=0, 2*n\3, print1(T(n,k), ", ")); print); \\ _Michel Marcus_, May 10 2018 %Y A304223 Row sums is A077953. %Y A304223 Cf. A304209. %K A304223 tabf,easy,sign %O A304223 0,4 %A A304223 _Shara Lalo_, May 08 2018