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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A322909 The permanent of an n X n Toeplitz matrix M(n) whose first row consists of successive positive integer numbers 1, ..., n and whose first column consists of 1, n + 1, ..., 2*n - 1. 4
1, 1, 7, 100, 2840, 129428, 8613997, 791557152, 95921167710, 14818153059968, 2842735387366627, 663020104070865664, 184757202542187563476, 60623405966739216871680, 23135486197103263598936745, 10160292704659539620791062528, 5087671168376607498331875818106 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The matrix M(n) differs from that of A306457 in using successive positive integers in place of successive prime numbers. [Modified by Stefano Spezia, Dec 20 2019 at the suggestion of Michel Marcus]

The trace of M(n) is A000027(n).

The sum of the first row of M(n) is A000217(n).

The sum of the first column of M(n) is A005448(n). [Corrected by Stefano Spezia, Dec 19 2019]

For n > 1, the sum of the superdiagonal of M(n) is A005843(n).

For n > 0, the sum of the (k-1)-th superdiagonal of M(n) is A003991(n,k). - Stefano Spezia, Dec 29 2019

For n > 1 and k > 0, the sum of the k-th subdiagonal of M(n) is A120070(n,k). - Stefano Spezia, Dec 31 2019

LINKS

Stefano Spezia, Table of n, a(n) for n = 0..35

Wikipedia, Toeplitz Matrix

EXAMPLE

For n = 1 the matrix M(1) is

   1

with permanent a(1) = 1.

For n = 2 the matrix M(2) is

   1, 2

   3, 1

with permanent a(2) = 7.

For n = 3 the matrix M(3) is

   1, 2, 3

   4, 1, 2

   5, 4, 1

with permanent a(3) = 100.

MAPLE

with(LinearAlgebra):

a:= n-> `if`(n=0, 1, Permanent(ToeplitzMatrix([

         seq(i, i=2*n-1..n+1, -1), seq(i, i=1..n)]))):

seq(a(n), n = 0 .. 15);

MATHEMATICA

b[n_]:=n; a[n_]:=If[n==0, 1, Permanent[ToeplitzMatrix[Join[{b[1]}, Array[b, n-1, {n+1, 2*n-1}]], Array[b, n]]]]; Array[a, 15, 0]

PROG

(PARI) tm(n) = {my(m = matrix(n, n, i, j, if (i==1, j, if (j==1, n+i-1)))); for (i=2, n, for (j=2, n, m[i, j] = m[i-1, j-1]; ); ); m; }

a(n) = matpermanent(tm(n)); \\ Stefano Spezia, Dec 19 2019

CROSSREFS

Cf. A000027, A000217, A003991, A005448, A005843, A120070, A306457, A322908 (determinant of M(n)).

Sequence in context: A297151 A052752 A182529 * A165878 A175345 A142358

Adjacent sequences:  A322906 A322907 A322908 * A322910 A322911 A322912

KEYWORD

nonn

AUTHOR

Stefano Spezia, Dec 30 2018

EXTENSIONS

a(0) = 1 prepended by Stefano Spezia, Dec 19 2019

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 November 26 07:25 EST 2020. Contains 338632 sequences. (Running on oeis4.)