OFFSET
1,4
COMMENTS
Let p(n)=p(n,x) be the characteristic polynomial of the n-th principal submatrix. The zeros of p(n) are positive, and they interlace the zeros of p(n+1). See A202605 for a guide to related sequences.
REFERENCES
(For references regarding interlacing roots, see A202605.)
EXAMPLE
Top of the array:
1...-1
1...-2....1
1...-3....3....-1
1...-5....8....-5....1
1...-7....17...-17...7...-1
MATHEMATICA
t = {1, 0, 0}; t1 = Flatten[{t, t, t, t, t, t, t, t, t, t}];
f[k_] := t1[[k]];
U[n_] := NestList[Most[Prepend[#, 0]] &, #,
Length[#] - 1] &[Table[f[k], {k, 1, n}]];
L[n_] := Transpose[U[n]];
p[n_] := CharacteristicPolynomial[L[n].U[n], x];
c[n_] := CoefficientList[p[n], x]
TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
Table[c[n], {n, 1, 12}]
Flatten[%] (* A203946 *)
TableForm[Table[c[n], {n, 1, 10}]]
CROSSREFS
KEYWORD
tabf,sign
AUTHOR
Clark Kimberling, Jan 08 2012
STATUS
approved