OFFSET
1,3
COMMENTS
REFERENCES
(For references regarding interlacing roots, see A202605.)
EXAMPLE
Top of the array:
1.....-1
3.....-5.....1
18....-36....12....-1
162...-360...153...-22...1
MATHEMATICA
f[i_, j_] := 1; f[i_, i_] := 2 i - 1;
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
TableForm[m[8]] (* 8x8 principal submatrix *)
Flatten[Table[f[i, n + 1 - i],
{n, 1, 15}, {i, 1, n}]] (* A204160 *)
p[n_] := CharacteristicPolynomial[m[n], x];
c[n_] := CoefficientList[p[n], x]
TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
Table[c[n], {n, 1, 12}]
Flatten[%] (* A204161 *)
TableForm[Table[c[n], {n, 1, 10}]]
CROSSREFS
KEYWORD
tabl,sign
AUTHOR
Clark Kimberling, Jan 12 2012
STATUS
approved