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Number of nX3 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.
1

%I #4 Nov 14 2016 22:29:08

%S 0,19,544,13720,347116,8803344,223230876,5660949042,143557203008,

%T 3640498372990,92320193797850,2341167983288042,59370190792031534,

%U 1505581649925192516,38180374263992817136,968224459304580152320

%N Number of nX3 0..3 arrays with every element plus 1 mod 4 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

%C Column 3 of A278188.

%H R. H. Hardin, <a href="/A278184/b278184.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 31*a(n-1) -155*a(n-2) +301*a(n-3) +159*a(n-4) -2992*a(n-5) +9662*a(n-6) -29732*a(n-7) +126855*a(n-8) -280808*a(n-9) -58215*a(n-10) +1824424*a(n-11) -5134012*a(n-12) +7021960*a(n-13) -3782179*a(n-14) -161494*a(n-15) -12931*a(n-16) +1006187*a(n-17) +1090*a(n-18) -1012324*a(n-19) -2180228*a(n-20) +2329252*a(n-21) -1301360*a(n-22) +252136*a(n-23) +383856*a(n-24) +87584*a(n-25) -102976*a(n-26) +3840*a(n-27)

%e Some solutions for n=4

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

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

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

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

%Y Cf. A278188.

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 14 2016