A204160 Symmetric matrix based on f(i,j)=(3i-2 if i=j and = 0 otherwise), by antidiagonals.

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

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: A359594 A368331 A366145 * A360165 A336870 A184101

Adjacent sequences: A204157 A204158 A204159 * A204161 A204162 A204163

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 12 2012

Status

approved