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%I #7 Jul 12 2012 00:39:54
%S 1,-1,-11,-6,1,40,70,15,-1,-116,-328,-240,-28,1,304,1176,1456,610,45,
%T -1,-752,-3680,-6408,-4704,-1295,-66,1,1792,10592,23760,25080,12432,
%U 2436,91,-1,-4160,-28800,-79040
%N Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of max{3i+j-3,i+3j-3} (A204008).
%C Let p(n)=p(n,x) be the characteristic polynomial of the n-th principal submatrix. The zeros of p(n) are real, 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 -11....-6.....1
%e 40.....70....15....-1
%e -116...-328..-240....1
%t f[i_, j_] := Max[3 i + j - 3, 3 j + i - 3];
%t m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t TableForm[m[6]] (* 6x6 principal submatrix *)
%t Flatten[Table[f[i, n + 1 - i],
%t {n, 1, 12}, {i, 1, n}]] (* A204008 *)
%t p[n_] := CharacteristicPolynomial[m[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}]
%t Flatten[%] (* A204011 *)
%t TableForm[Table[c[n], {n, 1, 10}]]
%Y Cf. A204008, A202605.
%K tabl,sign
%O 1,3
%A _Clark Kimberling_, Jan 09 2012
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