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!)
A283795 Triangle T(n,k) read by rows: the number of q-circulant n X n {0,1}-matrices where each row sum and each column sum equals k. 3
1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 8, 14, 8, 1, 1, 20, 40, 40, 20, 1, 1, 12, 42, 44, 42, 12, 1, 1, 42, 126, 210, 210, 126, 42, 1, 1, 32, 136, 224, 350, 224, 136, 32, 1, 1, 54, 216, 546, 756, 756, 546, 216, 54, 1, 1, 40, 260, 480, 1200, 1032, 1200, 480, 260, 40, 1, 1, 110, 550, 1650, 3300, 4620, 4620, 3300, 1650, 550, 110, 1, 1, 48, 324, 992, 2538, 3168 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

q-circulant matrices are constructed by fixing the first row and obtaining the remaining n-1 rows by circularly shifting values by q columns, any q from 0 to n-1.

The triangle is symmetric in each row because flipping 1's and 0's in a matrix gives also a circulant matrix with n-k ones in each row and column.

The number of 1-circulant matrices with k zeros in each row and each column is apparently given by Pascal's Triangle.

Is the column k=1 given by A002618?

LINKS

Table of n, a(n) for n=0..83.

P. Zellini, On some properties of circulant matrices, Lin. Alg. Applic. 26 (1979) 31-43

EXAMPLE

The triangle starts in row n=0 and column k=0 as:

1 rsum= 1

1 1 rsum= 2

1 2 1 rsum= 4

1 6 6 1 rsum= 14

1 8 14 8 1 rsum= 32

1 20 40 40 20 1 rsum= 122

1 12 42 44 42 12 1 rsum= 154

1 42 126 210 210 126 42 1 rsum= 758

1 32 136 224 350 224 136 32 1 rsum= 1136

1 54 216 546 756 756 546 216 54 1 rsum= 3146

CROSSREFS

Cf. A045655.

Sequence in context: A140956 A166919 A260238 * A168641 A255914 A143185

Adjacent sequences:  A283792 A283793 A283794 * A283796 A283797 A283798

KEYWORD

nonn,tabl

AUTHOR

R. J. Mathar, Mar 16 2017

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 September 27 10:35 EDT 2020. Contains 337380 sequences. (Running on oeis4.)