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A235510 Number of (n+1) X (1+1) 0..1 arrays with the sum of each 2 X 2 subblock maximum and minimum lexicographically nondecreasing rowwise and columnwise. 2

%I

%S 16,58,209,746,2660,9476,33753,120216,428160,1524918,5431081,19343086,

%T 68891428,245360464,873864257,3112313708,11084669648,39478636370,

%U 140605248417,500773018002,1783529550852,6352134688572,22623463167433

%N Number of (n+1) X (1+1) 0..1 arrays with the sum of each 2 X 2 subblock maximum and minimum lexicographically nondecreasing rowwise and columnwise.

%C Column 1 of A235517.

%H R. H. Hardin, <a href="/A235510/b235510.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 6*a(n-3) + a(n-4) + 2*a(n-5).

%F Conjectures from _Colin Barker_, Mar 19 2018: (Start)

%F G.f.: x*(16 - 6*x - 23*x^2 + 6*x^3 + 8*x^4) / ((1 - x)^2*(1 + x)*(1 - 3*x - 2*x^2)).

%F a(n) = (1/544)*(-221 - 68*(-1)^n + 2^(-1-n)*((2533-611*sqrt(17))*(3-sqrt(17))^n + (3+sqrt(17))^n*(2533+611*sqrt(17))) - 68*(1+n)).

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A235517.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 11 2014

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Last modified January 19 06:18 EST 2022. Contains 350464 sequences. (Running on oeis4.)