A300642 - OEIS

%I #4 Mar 10 2018 10:37:44

%S 0,4,10,64,316,1789,9738,54293,300456,1669005,9263141,51430163,

%T 285537725,1585321263,8801860535,48868792430,271324801628,

%U 1506424664770,8363834463324,46436926280661,257822913340328,1431461142742217

%N Number of nX4 0..1 arrays with every element equal to 2, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Column 4 of A300646.

%H R. H. Hardin, <a href="/A300642/b300642.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) +14*a(n-2) -17*a(n-3) -61*a(n-4) -49*a(n-5) -105*a(n-6) +151*a(n-7) +775*a(n-8) -58*a(n-9) -91*a(n-10) +1887*a(n-11) +512*a(n-12) +3274*a(n-13) +4088*a(n-14) -20637*a(n-15) -27360*a(n-16) -8376*a(n-17) -17162*a(n-18) +51171*a(n-19) +48004*a(n-20) +30560*a(n-21) +10871*a(n-22) -11625*a(n-23) -52251*a(n-24) -27283*a(n-25) -19433*a(n-26) -23710*a(n-27) +5592*a(n-28) +7218*a(n-29) -6323*a(n-30) +15212*a(n-31) +2942*a(n-32) -88*a(n-33) +4031*a(n-34) -1521*a(n-35) +534*a(n-36) -205*a(n-37) -151*a(n-38) +48*a(n-39) -135*a(n-40) +10*a(n-41) -47*a(n-42) +44*a(n-43) -13*a(n-44) -8*a(n-45) +12*a(n-46) -3*a(n-47) -2*a(n-48) +a(n-49)

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A300646.

%K nonn

%O 1,2

%A _R. H. Hardin_, Mar 10 2018