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!)
A204181 Symmetric matrix based on f(i,j) defined by f(i,1)=f(1,j)=1; f(i,i)= 2i-1; f(i,j)=0 otherwise; by antidiagonals. 3
1, 1, 1, 1, 3, 1, 1, 0, 0, 1, 1, 0, 5, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 7, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 9, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 11, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

A204181 represents the matrix M given by f(i,j) for i>=1 and j>=1.  See A204182 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..98.

EXAMPLE

Northwest corner:

1 1 1 1 1 1 1 1

1 3 0 0 0 0 0 0

1 0 5 0 0 0 0 0

1 0 0 7 0 0 0 0

1 0 0 0 9 0 0 0

MATHEMATICA

f[i_, j_] := 0; f[1, j_] := 1;

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

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}]]  (* A204181 *)

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[%]                 (* A204182 *)

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

CROSSREFS

Cf. A204182, A204016, A202453.

Sequence in context: A115717 A339632 A115718 * A204242 A211313 A321609

Adjacent sequences:  A204178 A204179 A204180 * A204182 A204183 A204184

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 12 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 May 12 09:16 EDT 2021. Contains 343821 sequences. (Running on oeis4.)