login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A204028 Symmetric matrix based on f(i,j)=min(3i-2,3j-2), by antidiagonals. 4
1, 1, 1, 1, 4, 1, 1, 4, 4, 1, 1, 4, 7, 4, 1, 1, 4, 7, 7, 4, 1, 1, 4, 7, 10, 7, 4, 1, 1, 4, 7, 10, 10, 7, 4, 1, 1, 4, 7, 10, 13, 10, 7, 4, 1, 1, 4, 7, 10, 13, 13, 10, 7, 4, 1, 1, 4, 7, 10, 13, 16, 13, 10, 7, 4, 1, 1, 4, 7, 10, 13, 16, 16, 13, 10, 7, 4, 1, 1, 4, 7, 10, 13, 16, 19, 16 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

A204028 represents the matrix M given by f(i,j)=min(3i-2,3j-2) for i>=1 and j>=1.  See A204029 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..86.

EXAMPLE

Northwest corner:

1...1...1...1....1....1

1...4...4...4....4....4

1...4...7...7....7....7

1...4...7...10...10...10

1...4...7...10...13...13

MATHEMATICA

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

m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]

TableForm[m[6]] (* 6x6 principal submatrix *)

Flatten[Table[f[i, n + 1 - i],

  {n, 1, 15}, {i, 1, n}]]  (* A204028 *)

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[%]                 (* A204029 *)

TableForm[Table[c[n], {n, 1, 10}]]

CROSSREFS

Cf. A204029, A204016, A202453.

Sequence in context: A046569 A046596 A174093 * A106314 A152716 A298575

Adjacent sequences:  A204025 A204026 A204027 * A204029 A204030 A204031

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 11 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 17 02:22 EST 2020. Contains 331976 sequences. (Running on oeis4.)