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Number of (n+1)X(3+1) 0..3 arrays with every 2X2 subblock summing to 5 6 or 7
1

%I #8 Aug 22 2019 20:35:41

%S 9124,385704,17309672,796635224,37078015004,1734708707700,

%T 81356563852940,3819965043029148,179459290594576812,

%U 8433120201697489676,396339147306043331956,18628300842155979771596,875574504616798793124900

%N Number of (n+1)X(3+1) 0..3 arrays with every 2X2 subblock summing to 5 6 or 7

%C Column 3 of A251381

%H R. H. Hardin, <a href="/A251376/b251376.txt">Table of n, a(n) for n = 1..210</a>

%H R. H. Hardin, <a href="/A251376/a251376.txt">Empirical recurrence of order 52</a>

%H Robert Israel, <a href="/A251376/a251376.pdf">Maple-assisted proof of empirical recurrence</a>

%F Empirical recurrence of order 52 (see link above)

%F Empirical recurrence verified (see link). - _Robert Israel_, Aug 22 2019

%e Some solutions for n=1

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

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

%p Rows:= [seq(seq(seq(seq([a,b,c,d],a=0..3),b=0..3),c=0..3),d=0..3)]:

%p f:= proc(i,j) local S,k;

%p S:= [seq(Rows[i][k]+Rows[i][k+1]+Rows[j][k]+Rows[j][k+1], k=1..3)];

%p if min(S)>=5 and max(S)<=7 then 1 else 0 fi

%p end proc:

%p T:= Matrix(256,256,f):

%p U[0]:= Vector(256,1):

%p for j from 1 to 40 do U[j]:= T . U[j-1] od:

%p seq(U[0]^%T . U[j], j=1..40); # _Robert Israel_, Aug 22 2019

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 01 2014