cp's OEIS Frontend

A185536 1/6 the number of nX3 0..5 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

%I A185536 #9 Jul 22 2025 09:53:29
%S A185536 1,110,2990,127570,4403225,167398110,6079401960,225574291125,
%T A185536 8285469213945,305786452982260,11260066599241195,415073544779136460,
%U A185536 15292958690004125565,563586551260018728505,20767361004817999220125
%N A185536 1/6 the number of nX3 0..5 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.
%C A185536 Column 3 of A185540
%H A185536 R. H. Hardin, <a href="/A185536/b185536.txt">Table of n, a(n) for n = 1..200</a>
%F A185536 Empirical: a(n)=22*a(n-1)+638*a(n-2)-2567*a(n-3)-29583*a(n-4)+27088*a(n-5)+209637*a(n-6)+620796*a(n-7)-1634411*a(n-8)-4083145*a(n-9)+17086070*a(n-10)-21827225*a(n-11)-42404829*a(n-12)-73933685*a(n-13)+687497360*a(n-14)-669370750*a(n-15)-1844490625*a(n-16)+8145764375*a(n-17)+6297734375*a(n-18)-14443984375*a(n-19)-34831953125*a(n-20)-42570312500*a(n-21)-47656250000*a(n-22)-78125000000*a(n-23)
%e A185536 Some solutions for 5X3 with a(1,1)=0
%e A185536 ..0..0..0....0..0..0....0..0..3....0..0..3....0..0..0....0..0..0....0..3..3
%e A185536 ..0..3..3....0..3..3....0..0..3....0..3..3....0..3..3....0..3..3....0..0..0
%e A185536 ..4..0..0....4..1..3....3..3..1....1..0..0....0..2..2....2..2..3....5..2..0
%e A185536 ..4..4..4....4..1..0....5..5..1....1..1..2....3..4..2....2..4..0....5..2..2
%e A185536 ..5..5..4....0..0..0....4..4..4....5..5..2....3..4..4....2..4..0....5..5..5
%K A185536 nonn
%O A185536 1,2
%A A185536 _R. H. Hardin_ Jan 30 2011