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A204160 Symmetric matrix based on f(i,j)=(3i-2 if i=j and = 0 otherwise), by antidiagonals. 3
1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 16, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

A204160 represents the matrix M given by f(i,j)=(3i-2 if i=j and = 0 otherwise) for i>=1 and j>=1.  See A204161 for characteristic polynomials of principal submatrices of M, with interlacing zeros.  See A204016 for a guide to other choices of M.

LINKS

Table of n, a(n) for n=1..97.

EXAMPLE

Northwest corner:

1 1 1 1

1 4 1 1

1 1 7 1

1 1 1 10

MATHEMATICA

f[i_, j_] := 1; f[i_, i_] := 3 i - 2;

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

Cf. A204161, A204016, A202453.

Sequence in context: A103524 A110916 A185058 * A184101 A164561 A178764

Adjacent sequences:  A204157 A204158 A204159 * A204161 A204162 A204163

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 12 2012

STATUS

approved

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Last modified April 19 16:18 EDT 2019. Contains 322282 sequences. (Running on oeis4.)