A197231 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,3,0,1,2 for x=0,1,2,3,4

3, 31, 242, 2117, 17759, 141210, 1207249, 10193669, 85161702, 716691651, 6018972449, 50526364522, 424443693477, 3564252187315, 29932907855790, 251391944508773, 2111203108705289, 17730374106602548, 148903966138218485

Offset

1,1

Comments

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 1's, every 4 is next to 4 2's

Column 4 of A197235

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +20*a(n-2) +203*a(n-3) +427*a(n-4) +1537*a(n-5) +2218*a(n-6) +12010*a(n-7) +55264*a(n-8) +77534*a(n-9) -32961*a(n-10) -537427*a(n-11) -865018*a(n-12) -747176*a(n-13) -526116*a(n-14) -4092226*a(n-15) -9500764*a(n-16) +29669226*a(n-17) +15689405*a(n-18) -110547100*a(n-19) -308503168*a(n-20) -308638276*a(n-21) +609211457*a(n-22) +779454919*a(n-23) +277475710*a(n-24) +1500049303*a(n-25) +9861087356*a(n-26) +20730905907*a(n-27) +22678007834*a(n-28) -5412857709*a(n-29) -15789571643*a(n-30) +41964885845*a(n-31) +42913198864*a(n-32) -135205920257*a(n-33) -438268865283*a(n-34) -234659296698*a(n-35) -184316815709*a(n-36) -810118777508*a(n-37) -470315764383*a(n-38) +1122593865379*a(n-39) +1334702800434*a(n-40) -1152188071272*a(n-41) +427833359703*a(n-42) +5042983854941*a(n-43) +4356486612154*a(n-44) -2037109587322*a(n-45) -5372301005081*a(n-46) -1153254231822*a(n-47) -1553204100836*a(n-48) -11005586699252*a(n-49) -10740079931534*a(n-50) +1464408422479*a(n-51) +7727385022685*a(n-52) +12295729031871*a(n-53) +10674432941965*a(n-54) +15051114410120*a(n-55) +6044687953781*a(n-56) -4823386540123*a(n-57) -6102759678547*a(n-58) -4035723334640*a(n-59) -8938890488658*a(n-60) -578317075744*a(n-61) -857748199466*a(n-62) +2521320540172*a(n-63) -473323601399*a(n-64) +682867934051*a(n-65) +206915320653*a(n-66) -827119502706*a(n-67) +134976154575*a(n-68) -115377036602*a(n-69) +152851153424*a(n-70) -19076781490*a(n-71) +26354396095*a(n-72) +2774183422*a(n-73) +6242349930*a(n-74) +2462273665*a(n-75) -1689740130*a(n-76) -477047513*a(n-77) -119416737*a(n-78) +8209997*a(n-79) +11583020*a(n-80) +1898284*a(n-81) +278464*a(n-82) +6016*a(n-83)

Example

Some solutions for n=5
..2..0..1..0....0..0..0..2....2..0..1..0....0..0..0..0....0..0..0..0
..0..1..3..1....2..0..0..0....0..2..3..1....1..3..1..0....0..0..0..0
..0..1..0..0....2..0..1..0....0..1..1..0....0..1..0..1....0..1..3..1
..2..3..1..0....0..1..3..2....0..3..1..0....0..0..1..3....0..2..1..0
..0..1..0..0....0..0..1..0....0..1..0..2....2..0..0..1....2..0..2..0

Crossrefs

Sequence in context: A121147 A114654 A198151 * A334980 A111400 A057972

Adjacent sequences: A197228 A197229 A197230 * A197232 A197233 A197234

Keyword

nonn

Author

R. H. Hardin Oct 12 2011

Status

approved