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 A204112 #9 Aug 02 2019 04:12:28 %S A204112 1,1,1,1,2,1,1,1,1,1,1,1,3,1,1,1,2,1,1,2,1,1,1,1,5,1,1,1,1,1,1,1,1,1, %T A204112 1,1,1,2,3,1,8,1,3,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,13,1,1,1,1,1,1,2, %U A204112 1,5,2,1,1,2,5,1,2,1,1,1,3,1,1,1,21,1,1,1,3,1,1,1,1,1,1,1,1,1 %N A204112 Symmetric matrix based on f(i,j) = gcd(F(i+1), F(j+1)), where F=A000045 (Fibonacci numbers), by antidiagonals. %C A204112 A204112 represents the matrix M given by f(i,j) = gcd(F(i+1), F(j+1)) for i >= 1 and j >= 1. See A204113 for characteristic polynomials of principal submatrices of M, with interlacing zeros. See A204016 for a guide to other choices of M. %e A204112 Northwest corner: %e A204112 1 1 1 1 1 1 %e A204112 1 2 1 1 2 1 %e A204112 1 1 3 1 1 1 %e A204112 1 1 1 5 1 1 %e A204112 1 2 1 1 8 1 %e A204112 1 1 1 1 1 13 %t A204112 u[n_] := Fibonacci[n + 1] %t A204112 f[i_, j_] := GCD[u[i], u[j]]; %t A204112 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}] %t A204112 TableForm[m[8]] (* 8 X 8 principal submatrix *) %t A204112 Flatten[Table[f[i, n + 1 - i], %t A204112 {n, 1, 15}, {i, 1, n}]] (* A204112 *) %t A204112 p[n_] := CharacteristicPolynomial[m[n], x]; %t A204112 c[n_] := CoefficientList[p[n], x] %t A204112 TableForm[Flatten[Table[p[n], {n, 1, 10}]]] %t A204112 Table[c[n], {n, 1, 12}] %t A204112 Flatten[%] (* A204113 *) %t A204112 TableForm[Table[c[n], {n, 1, 10}]] %Y A204112 Cf. A204113, A204016, A202453. %K A204112 nonn,tabl %O A204112 1,5 %A A204112 _Clark Kimberling_, Jan 11 2012