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A263869 Number of (n+1) X (4+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits, and rows and columns lexicographically nondecreasing. 1

%I

%S 3,3,7,7,16,17,41,48,113,141,303,387,752,962,1713,2175,3607,4531,7095,

%T 8811,13168,16171,23257,28262,39365,47373,64223,76599,101472,120036,

%U 155873,183005,233547,272307,342247,396511,491664,566277,693769,794716

%N Number of (n+1) X (4+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits, and rows and columns lexicographically nondecreasing.

%H R. H. Hardin, <a href="/A263869/b263869.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 5*a(n-2) - 12*a(n-3) - 9*a(n-4) + 30*a(n-5) + 5*a(n-6) - 40*a(n-7) + 5*a(n-8) + 30*a(n-9) - 9*a(n-10) - 12*a(n-11) + 5*a(n-12) + 2*a(n-13) - a(n-14).

%F Conjectures from _Colin Barker_, Jan 03 2019: (Start)

%F G.f.: x*(3 - 3*x - 14*x^2 + 14*x^3 + 30*x^4 - 29*x^5 - 31*x^6 + 31*x^7 + 20*x^8 - 20*x^9 - 7*x^10 + 7*x^11 + x^12 - x^13) / ((1 - x)^8*(1 + x)^6).

%F a(n) = (315*(2889-841*(-1)^n) + (537927 - 96327*(-1)^n)*n - 21*(-4723+755*(-1)^n)*n^2 - 7*(-1469 + 45*(-1)^n)*n^3 - 105*(3+5*(-1)^n)*n^4 - 7*(-29+9*(-1)^n)*n^5 + 42*n^6 + 2*n^7) / 645120.

%F (End)

%e Some solutions for n=4:

%e ..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0

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

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

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

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

%Y Column 4 of A263873.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 28 2015

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Last modified October 3 13:20 EDT 2022. Contains 357237 sequences. (Running on oeis4.)