A196726 - OEIS

%I #5 Mar 31 2012 12:36:27

%S 6,101,2025,30971,547874,9376754,155884161,2642927522,44901935948,

%T 759934568782,12869664286125,217998199717188,3691905169363581,

%U 62529315118785567,1059069284509026344,17937180980623591659

%N Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,4,0,3 for x=0,1,2,3,4

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

%C Column 5 of A196729

%H R. H. Hardin, <a href="/A196726/b196726.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 3*a(n-1) +99*a(n-2) +1441*a(n-3) +9542*a(n-4) +65340*a(n-5) +375237*a(n-6) +1283527*a(n-7) -3033844*a(n-8) -38745519*a(n-9) -43843108*a(n-10) +302033296*a(n-11) +391928176*a(n-12) -1957031993*a(n-13) -1631575573*a(n-14) +15853193792*a(n-15) +22009315053*a(n-16) -92735357332*a(n-17) -245935500390*a(n-18) -86252266496*a(n-19) +35130256366*a(n-20) +972260853374*a(n-21) +3276955967914*a(n-22) -6610716955874*a(n-23) -3525699233277*a(n-24) +65567179726380*a(n-25) -15722559067129*a(n-26) -114572567130619*a(n-27) +281819707107586*a(n-28) -42180488958937*a(n-29) -276357272239307*a(n-30) +596218335367780*a(n-31) -105577240614858*a(n-32) -615148787787340*a(n-33) +774952557949439*a(n-34) -270977886635686*a(n-35) -409786103321288*a(n-36) +894803816081140*a(n-37) -501563532236944*a(n-38) -84085834331876*a(n-39) +856139262759798*a(n-40) -512778230035747*a(n-41) +188441933273535*a(n-42) +338907502462032*a(n-43) -594272969260236*a(n-44) +446581290575878*a(n-45) +119041366608427*a(n-46) -501347912648361*a(n-47) +437989765858148*a(n-48) +179856505419600*a(n-49) -263898453871463*a(n-50) +185394293683331*a(n-51) +129885852292572*a(n-52) -77565539079531*a(n-53) +75493187658810*a(n-54) +42047007188453*a(n-55) -10185784471731*a(n-56) +20133457876007*a(n-57) +7243328031182*a(n-58) +934687323526*a(n-59) +3158316425239*a(n-60) +1070440379101*a(n-61) +298956128968*a(n-62) +194101359866*a(n-63) +135738438260*a(n-64) +4541615765*a(n-65) -1005336253*a(n-66) -950389008*a(n-67) +559575055*a(n-68) -457730683*a(n-69) -463176209*a(n-70) -205291389*a(n-71) -33500884*a(n-72) +3474684*a(n-73) -151612*a(n-74) -522331*a(n-75) -234699*a(n-76) +13407*a(n-77) +11219*a(n-78) +3256*a(n-79) +224*a(n-80)

%e Some solutions for n=4

%e ..0..0..1..1..0....0..0..0..0..0....0..3..0..1..0....1..1..0..0..0

%e ..3..0..0..0..0....0..3..3..0..1....0..0..0..1..0....0..0..0..0..0

%e ..0..1..3..0..0....1..0..0..0..1....3..0..3..0..1....1..0..0..0..3

%e ..0..1..0..3..0....1..0..3..0..0....0..1..1..0..1....1..0..0..3..0

%K nonn

%O 1,1

%A _R. H. Hardin_ Oct 05 2011