|
%I #5 Mar 31 2012 12:36:27
%S 3,23,104,815,3675,20500,115563,638791,3550336,19599537,108573593,
%T 601527392,3331391577,18450904073,102183492764,565933465777,
%U 3134368803899,17359289108840,96142199882539,532471005541643
%N Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,3,0,2,1 for x=0,1,2,3,4
%C Every 0 is next to 0 4's, every 1 is next to 1 3's, every 2 is next to 2 0's, every 3 is next to 3 2's, every 4 is next to 4 1's
%C Column 4 of A196974
%H R. H. Hardin, <a href="/A196970/b196970.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 2*a(n-1) +10*a(n-2) +26*a(n-3) +94*a(n-4) +278*a(n-5) +224*a(n-6) -20*a(n-7) -215*a(n-8) -2611*a(n-9) -6490*a(n-10) -7574*a(n-11) -5938*a(n-12) -3047*a(n-13) +5*a(n-14) +8878*a(n-15) +11607*a(n-16) +15885*a(n-17) +40601*a(n-18) +29465*a(n-19) +25039*a(n-20) +28387*a(n-21) -11472*a(n-22) -18764*a(n-23) -4729*a(n-24) -4778*a(n-25) -46385*a(n-26) -52772*a(n-27) +249*a(n-28) -4390*a(n-29) -40819*a(n-30) -11260*a(n-31) +9680*a(n-32) +11092*a(n-33) +13114*a(n-34) +10779*a(n-35) +2141*a(n-36) -2135*a(n-37) -1428*a(n-38) +604*a(n-39) +466*a(n-40) -428*a(n-41) +101*a(n-42) +108*a(n-43) -72*a(n-44) -16*a(n-45) +5*a(n-46)
%e Some solutions for n=5
%e ..0..2..0..2....2..0..0..0....2..0..2..0....2..0..0..2....0..0..0..2
%e ..0..3..2..0....0..0..2..2....0..0..2..0....0..0..0..0....0..0..0..0
%e ..0..2..3..0....0..2..1..0....2..2..2..0....0..2..3..2....0..2..2..0
%e ..0..0..2..2....0..2..3..2....0..0..0..0....1..3..2..0....2..3..2..0
%e ..2..0..0..0....0..0..2..0....0..0..0..2....0..2..0..2....0..0..0..0
%K nonn
%O 1,1
%A _R. H. Hardin_ Oct 08 2011
| 