|
%I #9 Dec 03 2022 12:09:34
%S 1,6,13,22,60,147,310,723,1723,3917,8973,20875,48427,111384,256857,
%T 599340,1384994,3187563,7469888,17334233,39905291,94076289,219435873,
%U 505824167,1202595689,2825927772,6530389759,15704159500,37297212976
%N Number of n X 5 binary arrays with every 1 having exactly three king-move neighbors equal to 1.
%C Column 5 of A183456.
%H R. H. Hardin, <a href="/A183452/b183452.txt">Table of n, a(n) for n = 1..200</a>
%F Conjecture: g.f. -x*(1 +5*x +607360*x^20 -11532*x^9 +753306*x^19 +6*x^2 -288*x^26 -57080*x^10 -612804*x^16 +7234*x^8 -600857*x^17 +181998*x^18 -57*x^3 -10592*x^25 -16800*x^24 -182104*x^23 -283*x^4 +5942*x^7 -132231*x^15 -345*x^5 +1200*x^6+ 285093*x^14 +259034*x^13 +52803*x^12 +384*x^29 +768*x^28 +2048*x^27 -67623*x^11 -344072*x^22 -99176*x^21)/(-1 +x +275562*x^20 +15867*x^9 -37876*x^19 +x^2 -8768*x^26 +384*x^30 -7896*x^10 -20075*x^16 +1261*x^8 -184239*x^17 -567185*x^18 +60*x^3 -8096*x^25 -174456*x^24 -168944*x^23 -52*x^4+980*x^7 +311194*x^15-58*x^5 -1393*x^6 +65529*x^14 +24304*x^13 -94858*x^12 +384*x^29 +1664*x^28 -1952*x^27 -12862*x^11 +73800*x^22 +537480*x^21) . - _R. J. Mathar_, Dec 03 2022
%e Some solutions for 7X5
%e ..0..0..0..1..1....0..0..0..1..1....0..0..0..0..0....0..0..0..0..0
%e ..1..1..0..1..1....0..0..0..1..1....0..1..1..0..0....0..0..0..0..0
%e ..1..1..0..0..0....0..0..0..0..0....0..1..1..0..0....1..1..0..0..0
%e ..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....1..1..0..1..1
%e ..0..0..0..0..0....0..0..0..0..0....1..1..0..0..0....0..0..0..1..1
%e ..1..1..0..1..1....0..0..0..1..1....1..1..0..1..1....1..1..0..0..0
%e ..1..1..0..1..1....0..0..0..1..1....0..0..0..1..1....1..1..0..0..0
%K nonn
%O 1,2
%A _R. H. Hardin_, Jan 05 2011
| 