_R. H. Hardin (rhhardin(AT)att.net) _ Oct 19 2011

editing

approved

R. H. Hardin, <a href="/A197892/b197892.txt">Table of n, a(n) for n = 1..210</a>

allocated Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,3,0,1,1 for Ron Hardinx=0,1,2,3,4

3, 31, 180, 1141, 7589, 46988, 307547, 2021039, 13090390, 85028181, 551562559, 3578528548, 23237970485, 150848706421, 979297967866, 6357554112195, 41269666346783, 267909267230378, 1739184952510823, 11290199883542271

1,1

Every 0 is next to 0 3's, every 1 is next to 1 3's, every 2 is next to 2 0's, every 3 is next to 3 1's, every 4 is next to 4 1's

Column 4 of A197896

Empirical: a(n) = 2*a(n-1) +7*a(n-2) +85*a(n-3) +131*a(n-4) +1031*a(n-5) +2337*a(n-6) +8550*a(n-7) +12720*a(n-8) -2503*a(n-9) -69815*a(n-10) -182341*a(n-11) -349302*a(n-12) -701378*a(n-13) -1194928*a(n-14) -1520524*a(n-15) +1104029*a(n-16) +9517101*a(n-17) +20414166*a(n-18) +28681507*a(n-19) +31397053*a(n-20) +47109328*a(n-21) +83552413*a(n-22) +50410776*a(n-23) -175601607*a(n-24) -602103463*a(n-25) -1113255961*a(n-26) -1294864872*a(n-27) -1661936007*a(n-28) -1575532919*a(n-29) +1059361172*a(n-30) +6451468333*a(n-31) +9171362882*a(n-32) -1638592507*a(n-33) -17030822828*a(n-34) -16695990727*a(n-35) +7575488619*a(n-36) +25627349643*a(n-37) +10076727373*a(n-38) -17838315970*a(n-39) -20360343191*a(n-40) -163931400*a(n-41) +10227773583*a(n-42) +3174212699*a(n-43) -2366570207*a(n-44) +3051844937*a(n-45) +6136022556*a(n-46) +320032620*a(n-47) -3775982947*a(n-48) -740275299*a(n-49) +1574729140*a(n-50) -363120361*a(n-51) -1201514175*a(n-52) -80552012*a(n-53) +283808369*a(n-54) -137880828*a(n-55) -85333300*a(n-56) +49138245*a(n-57) -2532444*a(n-58) +17327284*a(n-59) +4875438*a(n-60) +2784554*a(n-61) +171416*a(n-62) -93195*a(n-63) -24535*a(n-64) -38680*a(n-65) -6704*a(n-66) -1216*a(n-67)

Some solutions containing all values 0 to 4 for n=5

..1..3..1..0....2..0..0..1....1..3..1..0....0..1..0..2....1..3..1..0

..1..1..4..1....0..0..1..3....0..1..4..1....2..3..1..0....0..1..4..1

..3..1..1..3....0..1..4..1....0..2..1..3....0..1..4..1....0..2..1..3

..1..0..0..1....2..3..1..0....0..0..0..1....0..0..1..3....0..0..0..1

..0..2..2..0....0..1..0..0....0..0..0..0....2..0..0..1....0..2..2..0

allocated

nonn

R. H. Hardin (rhhardin(AT)att.net) Oct 19 2011

approved

editing

allocated for Ron Hardin

allocated

approved