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A251160 Number of (n+1)X(1+1) 0..3 arrays with no 2X2 subblock having the maximum of its diagonal elements greater than the absolute difference of its antidiagonal elements 1

%I

%S 96,552,2658,12001,55131,257417,1201970,5597648,26056421,121329295,

%T 565030902,2631278472,12253239453,57060424477,265717806149,

%U 1237389994220,5762253389058,26833543568447,124957900541999,581901431575301

%N Number of (n+1)X(1+1) 0..3 arrays with no 2X2 subblock having the maximum of its diagonal elements greater than the absolute difference of its antidiagonal elements

%C Column 1 of A251167

%H R. H. Hardin, <a href="/A251160/b251160.txt">Table of n, a(n) for n = 1..210</a>

%H Robert Israel, <a href="/A251160/a251160.pdf">Maple-assisted proof of empirical formula</a>

%F Empirical: a(n) = 7*a(n-1) -18*a(n-2) +43*a(n-3) -59*a(n-4) +70*a(n-5) -62*a(n-6) +33*a(n-7) -14*a(n-8) -3*a(n-9) +6*a(n-10) -a(n-11) for n>13.

%F Verified by _Robert Israel_, Jan 11 2019 (See link).

%e Some solutions for n=4

%e ..0..2....2..3....1..2....3..3....1..3....0..3....1..3....1..1....0..3....0..3

%e ..0..0....0..3....0..2....0..2....0..3....0..3....1..2....0..1....1..1....0..0

%e ..3..0....0..3....0..1....0..0....1..1....0..3....1..1....1..0....0..0....2..2

%e ..3..3....3..0....0..1....2..2....0..0....0..1....0..0....1..0....1..1....0..1

%e ..0..1....3..1....1..0....0..0....3..1....0..0....1..0....3..2....0..1....3..1

%p q:= proc(a,b) local a1, a2, b1, b2;

%p a1:= (a-1) mod 4; a2:= (a-1-a1)/4;

%p b1:= (b-1) mod 4; b2:= (b-1-b1)/4;

%p if max(b1,a2) > abs(b2-a1) then 0 else 1 fi

%p end proc:

%p T:= Matrix(16,16,q):

%p u:= Vector(16,1):

%p seq(u^%T . T^n . u, n=1..30); # _Robert Israel_, Jan 11 2019

%Y Cf. A251167.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 30 2014

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Last modified May 16 05:18 EDT 2022. Contains 353693 sequences. (Running on oeis4.)