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.
Array starts (m>=3, n>=0): 1 3 9 27 81 243 729 2187 6561 ... 1 4 14 50 178 634 2258 8042 28642 ... 1 5 19 75 295 1161 4569 17981 70763 ... 1 6 24 100 418 1748 7310 30570 127842 ... 1 7 29 125 543 2363 10287 44787 194995 ... 1 8 34 150 668 2986 13362 59816 267802 ... 1 9 39 175 793 3611 16475 75229 343633 ... 1 10 44 200 918 4236 19598 90790 420870 ...
diff = 2; m0 = 3; mmax = 12;
TransferGf[m_, u_, t_, v_, z_] := Array[u, m].LinearSolve[IdentityMatrix[m] - z*Array[t, {m, m}], Array[v, m]]
RowGf[d_, m_, z_] := 1+z*TransferGf[m, 1&, Boole[Abs[#1-#2] <= d]&, 1&, z];
row[m_] := row[m] = CoefficientList[RowGf[diff, m, x] + O[x]^mmax, x];
T[m_ /; m >= m0, n_ /; n >= 0] := row[m][[n + 1]];
Table[T[m - n , n], {m, m0, mmax}, {n, m - m0, 0, -1}] // Flatten (* Jean-François Alcover, Jun 17 2017, adapted from PARI *)
TransferGf(m,u,t,v,z)=vector(m,i,u(i))*matsolve(matid(m)-z*matrix(m,m,i,j,t(i,j)),vectorv(m,i,v(i))); RowGf(d,m,z)=1+z*TransferGf(m, i->1, (i,j)->abs(i-j)<=d, j->1, z); for(m=3, 10, print(RowGf(2,m,x))); for(m=3, 10, v=Vec(RowGf(2,m,x) + O(x^9)); for(n=1, length(v), print1( v[n], ", ") ); print(); );
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