A196586 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,2,0,1,4 for x=0,1,2,3,4

3, 65, 698, 7407, 79091, 839370, 8980645, 96049685, 1025896374, 10959530915, 117114442817, 1251366955956, 13370045741595, 142856645330593, 1526402224409012, 16309198590770683, 174259846871282895

Offset

1,1

Comments

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

Column 4 of A196590

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 3*a(n-1) +30*a(n-2) +372*a(n-3) +1425*a(n-4) +4794*a(n-5) +5879*a(n-6) +53716*a(n-7) +69265*a(n-8) -55011*a(n-9) +464613*a(n-10) -775298*a(n-11) -4116069*a(n-12) -4062483*a(n-13) -17638119*a(n-14) -33560762*a(n-15) -90129391*a(n-16) -65437473*a(n-17) +43396713*a(n-18) -830601779*a(n-19) +856872781*a(n-20) +2726212008*a(n-21) -1469269304*a(n-22) +11347995087*a(n-23) +14640109580*a(n-24) -658490033*a(n-25) +24413623331*a(n-26) -1361732153*a(n-27) -43737289731*a(n-28) -20542155378*a(n-29) -39405283664*a(n-30) -119679395696*a(n-31) +12260927215*a(n-32) -21887393779*a(n-33) -370840837138*a(n-34) +524177033502*a(n-35) -127495983001*a(n-36) -719270733505*a(n-37) +975519231046*a(n-38) -1383301424729*a(n-39) +412344469559*a(n-40) +1477510270312*a(n-41) -2759075006772*a(n-42) +1558093761002*a(n-43) +642269999068*a(n-44) -1820967240539*a(n-45) +2189325682656*a(n-46) -832210546513*a(n-47) -1232354088968*a(n-48) +1579417078318*a(n-49) -881720240784*a(n-50) -118956472413*a(n-51) +1027124845779*a(n-52) -368226541476*a(n-53) +51953077965*a(n-54) -215342248390*a(n-55) -155072573300*a(n-56) -8736609974*a(n-57) +152582666460*a(n-58) +211899540641*a(n-59) -78130188431*a(n-60) -5381811852*a(n-61) -16590509749*a(n-62) -22553530010*a(n-63) +6426251424*a(n-64) -64602873*a(n-65) +5399215579*a(n-66) +1516459431*a(n-67) +544600608*a(n-68) -442634949*a(n-69) -782904614*a(n-70) -434916372*a(n-71) -368521520*a(n-72) -140271441*a(n-73) +34388261*a(n-74) +59381692*a(n-75) +20492904*a(n-76) +5879779*a(n-77) +1616338*a(n-78) +261744*a(n-79) -5040*a(n-80) +11232*a(n-81)

Example

Some solutions for n=5
..0..0..1..0....0..2..0..0....0..0..1..0....0..2..0..2....1..0..2..1
..0..0..2..0....0..1..0..0....0..0..2..1....0..1..0..0....2..0..0..1
..2..1..1..0....2..0..0..2....1..2..0..0....0..0..1..0....0..0..0..2
..0..1..1..2....2..0..0..1....1..2..0..0....1..2..2..0....0..2..2..0
..0..2..0..0....0..0..0..0....0..0..2..1....0..0..0..0....0..1..1..0

Crossrefs

Sequence in context: A326429 A300010 A196798 * A197043 A188984 A112000

Adjacent sequences: A196583 A196584 A196585 * A196587 A196588 A196589

Keyword

nonn

Author

R. H. Hardin Oct 04 2011

Status

approved