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%I #10 Jul 12 2012 00:39:54
%S 1,-1,1,-3,1,1,-6,5,-1,1,-13,18,-8,1,1,-24,52,-40,12,-1,1,-39,131,
%T -155,78,-16,1,1,-58,291,-508,391,-138,21,-1,1,-81,584,-1410,1548,
%U -840,225,-27,1,1,-108,1078,-3448,5151,-4016,1658,-348,33,-1,1
%N Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of A203949.
%C 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.
%D (For references regarding interlacing roots, see A202605.)
%e Top of the array:
%e 1...-1
%e 1...-3....1
%e 1...-6....5....-1
%e 1...-13....18...-8....1
%e 1...-24...52...-40...12...-1
%t t = {1, 1, 0}; t1 = Flatten[{t, t, t, t, t, t, t, t, t}];
%t f[k_] := t1[[k]];
%t U[n_] :=
%t NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[
%t Table[f[k], {k, 1, n}]];
%t L[n_] := Transpose[U[n]];
%t p[n_] := CharacteristicPolynomial[L[n].U[n], x];
%t c[n_] := CoefficientList[p[n], x]
%t TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t Table[c[n], {n, 1, 12}] (* A203950 *)
%t Flatten[%]
%t TableForm[Table[c[n], {n, 1, 10}]]
%Y Cf. A203949, A202605.
%K tabl,sign
%O 1,4
%A _Clark Kimberling_, Jan 08 2012
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