login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A181255 Number of (n+2) X 3 binary matrices with every 3 X 3 block having exactly four 1's. 1

%I #19 Feb 12 2023 10:53:41

%S 126,336,906,2484,7218,21024,61398,182520,542754,1614492,4829706,

%T 14448456,43225326,129555936,388309626,1163860164,3490511778,

%U 10468335024,31395421638,94176681480,282501311634,847417788972,2542167220986

%N Number of (n+2) X 3 binary matrices with every 3 X 3 block having exactly four 1's.

%C Column 1 of A181262.

%C The number of 1s in each row repeats with period 3, and we can divide the matrices into 12 classes (013, 022, 031, 103, 112, 121, 130, 202, 211, 220, 301, or 310) based on the pattern of row sums. The number of matrices in each class satisfies b(n) = 3*b(n-1), 3*b(n-3), or 9*b(n-3), depending on the number of 1s and 2s in the pattern. Therefore, the combined sequence satisfies [(T - 3I)(T^3 - 3I)(T^3 - 9I)](a)(n) = 0, where T is the right shift operator defined by T(a)(n) = a(n+1), and I is the identity operator. This is equivalent to the empirical formula for a(n) given below. - _David Radcliffe_, Jan 12 2023

%H R. H. Hardin, <a href="/A181255/b181255.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 3*a(n-1) + 12*a(n-3) - 36*a(n-4) - 27*a(n-6) + 81*a(n-7).

%F Empirical g.f.: 6*x*(21 - 7*x - 17*x^2 - 291*x^3 + 45*x^4 + 99*x^5 + 756*x^6) / ((1 - 3*x)*(1 - 3*x^3)*(1 - 9*x^3)). - _Colin Barker_, Mar 26 2018

%e Some solutions for 4 X 3:

%e 1 0 1 0 1 1 0 1 0 1 1 0 0 1 0 0 1 0 1 0 0

%e 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 0 1 0 0 0

%e 1 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 1

%e 1 1 0 1 1 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 1

%Y Cf. A181262.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 10 2010

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 25 12:33 EDT 2024. Contains 371969 sequences. (Running on oeis4.)