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Number of 4 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1, 2 or 3 neighboring 1's.
1

%I #6 May 04 2024 11:42:18

%S 1,126,1421,11024,131044,1580681,16899640,184447765,2071914854,

%T 22993996808,253857329257,2815072088290,31231596904276,

%U 346040351074271,3834662231710946,42507894984837013,471153783855939918

%N Number of 4 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1, 2 or 3 neighboring 1's.

%C Row 4 of A297654.

%H R. H. Hardin, <a href="/A297657/b297657.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) +15*a(n-2) +372*a(n-3) +1025*a(n-4) -46*a(n-5) -4101*a(n-6) -34244*a(n-7) -94085*a(n-8) -21654*a(n-9) +165356*a(n-10) +639904*a(n-11) +1471523*a(n-12) -895908*a(n-13) -4864047*a(n-14) -1270214*a(n-15) +3721117*a(n-16) +3725224*a(n-17) +1517589*a(n-18) -2895666*a(n-19) +611461*a(n-20) -1569477*a(n-21) -5436112*a(n-22) +6015995*a(n-23) -1131454*a(n-24) -3262066*a(n-25) +5806854*a(n-26) -3112355*a(n-27) -927930*a(n-28) +2386399*a(n-29) -1228290*a(n-30) -18124*a(n-31) +313018*a(n-32) -154300*a(n-33) +36726*a(n-34) +142*a(n-35) -2108*a(n-36) +652*a(n-37) +4*a(n-38).

%e Some solutions for n=5

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

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

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

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

%Y Cf. A297654.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 02 2018