login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A204022 Symmetric matrix based on f(i,j)=max(2i-1, 2j-1), by antidiagonals. 3
1, 3, 3, 5, 3, 5, 7, 5, 5, 7, 9, 7, 5, 7, 9, 11, 9, 7, 7, 9, 11, 13, 11, 9, 7, 9, 11, 13, 15, 13, 11, 9, 9, 11, 13, 15, 17, 15, 13, 11, 9, 11, 13, 15, 17, 19, 17, 15, 13, 11, 11, 13, 15, 17, 19, 21, 19, 17, 15, 13, 11, 13, 15, 17, 19, 21, 23, 21, 19, 17, 15, 13, 13, 15, 17 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A204022 represents the matrix M given by f(i,j)=max(2i-1,2j-1) for i>=1 and j>=1.  See A204023 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..75.

EXAMPLE

Northwest corner:

1 3 5 7 9

3 3 5 7 9

5 5 5 7 9

7 7 7 7 9

9 9 9 9 9

MATHEMATICA

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

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}]]          (* A204022 *)

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[%]                         (* A204023 *)

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

CROSSREFS

Cf. A204022, A204016, A202453.

Sequence in context: A158894 A131919 A185154 * A131832 A255316 A078587

Adjacent sequences:  A204019 A204020 A204021 * A204023 A204024 A204025

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 8 06:50 EST 2016. Contains 278902 sequences.