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 A204114 #9 Aug 02 2019 04:12:40 %S A204114 1,1,1,1,3,1,1,1,1,1,1,1,4,1,1,1,1,1,1,1,1,1,3,1,7,1,3,1,1,1,2,1,1,2, %T A204114 1,1,1,1,1,1,11,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,4,1,1,18,1,1,4,3,1,1, %U A204114 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,29,1,1,1,1,1,1,1,1,2,1,1,2,1 %N A204114 Symmetric matrix based on f(i,j) = gcd(L(i), L(j)), where L=A000032 (Lucas numbers), by antidiagonals. %C A204114 A204114 represents the matrix M given by f(i,j) = gcd(L(i+1), L(j+1)) for i >= 1 and j >= 1. See A204115 for characteristic polynomials of principal submatrices of M, with interlacing zeros. See A204016 for a guide to other choices of M. %e A204114 Northwest corner: %e A204114 1 1 1 1 1 %e A204114 1 3 1 1 1 %e A204114 1 1 4 1 1 %e A204114 1 1 1 7 1 %e A204114 1 1 1 1 11 %t A204114 u[n_] := LucasL[n] %t A204114 f[i_, j_] := GCD[u[i], u[j]]; %t A204114 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}] %t A204114 TableForm[m[8]] (* 8 X 8 principal submatrix *) %t A204114 Flatten[Table[f[i, n + 1 - i], %t A204114 {n, 1, 15}, {i, 1, n}]] (* A204114 *) %t A204114 p[n_] := CharacteristicPolynomial[m[n], x]; %t A204114 c[n_] := CoefficientList[p[n], x] %t A204114 TableForm[Flatten[Table[p[n], {n, 1, 10}]]] %t A204114 Table[c[n], {n, 1, 12}] %t A204114 Flatten[%] (* A204115 *) %t A204114 TableForm[Table[c[n], {n, 1, 10}]] %Y A204114 Cf. A204115, A204016, A202453. %K A204114 nonn,tabl %O A204114 1,5 %A A204114 _Clark Kimberling_, Jan 11 2012