A196481 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,2,1,4 for x=0,1,2,3,4

5, 36, 147, 826, 4344, 23930, 131650, 705342, 3801448, 20598890, 111440744, 603129471, 3265314697, 17669434957, 95611160941, 517439229137, 2800320468761, 15154923134842, 82016941366524, 443863716501084, 2402118373132479

Offset

1,1

Comments

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

Column 4 of A196485

Links

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

Formula

Empirical: a(n) = 7*a(n-1) -13*a(n-2) +35*a(n-3) -71*a(n-4) +130*a(n-5) -3*a(n-6) -1928*a(n-7) -1330*a(n-8) +1352*a(n-9) -4503*a(n-10) +22948*a(n-11) +78439*a(n-12) +18219*a(n-13) +176569*a(n-14) +270165*a(n-15) -965545*a(n-16) -751353*a(n-17) +1768039*a(n-18) -5921761*a(n-19) -17591901*a(n-20) +1660639*a(n-21) +38009387*a(n-22) +34944145*a(n-23) -29939486*a(n-24) -33288676*a(n-25) +129432090*a(n-26) +99083665*a(n-27) -232720951*a(n-28) -566879745*a(n-29) -1180155177*a(n-30) -1030424648*a(n-31) +979203466*a(n-32) +2456340934*a(n-33) +3736423491*a(n-34) +5528169516*a(n-35) +2286060502*a(n-36) -1315817384*a(n-37) -3941109379*a(n-38) -16050787304*a(n-39) -14470825352*a(n-40) +5826996088*a(n-41) +9873171482*a(n-42) +13067614247*a(n-43) +14595058730*a(n-44) -11260509982*a(n-45) -16917904933*a(n-46) +10812300576*a(n-47) +11951753951*a(n-48) -15435242911*a(n-49) -18696723805*a(n-50) +4775203461*a(n-51) +19908143079*a(n-52) +10291747605*a(n-53) -13249378754*a(n-54) -9916980184*a(n-55) +10390605400*a(n-56) +3188704533*a(n-57) -7483388917*a(n-58) -1297562823*a(n-59) +1371069449*a(n-60) +776611168*a(n-61) +1364676447*a(n-62) +42305803*a(n-63) -650437009*a(n-64) -16173641*a(n-65) +218648274*a(n-66) -99308591*a(n-67) -173381886*a(n-68) -13512178*a(n-69) +63351803*a(n-70) +20434324*a(n-71) -12476692*a(n-72) -6998032*a(n-73) +743752*a(n-74) +874450*a(n-75) -60717*a(n-76) -66780*a(n-77) +25889*a(n-78) +23539*a(n-79) -4938*a(n-80) -3321*a(n-81) +228*a(n-82) +246*a(n-83) -14*a(n-84) for n>86

Example

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

Crossrefs

Sequence in context: A275143 A276249 A027765 * A096945 A063417 A109726

Adjacent sequences: A196478 A196479 A196480 * A196482 A196483 A196484

Keyword

nonn

Author

R. H. Hardin Oct 03 2011

Status

approved