A195975 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,3,4 for x=0,1,2,3,4

9, 43, 67, 133, 244, 519, 1072, 2225, 4456, 9098, 19066, 39689, 82372, 171498, 358146, 748911, 1567225, 3279792, 6866722, 14390098, 30170057, 63261378, 132676528, 278340227, 584041659, 1225661652, 2572438981, 5399619168, 11334969352

Offset

1,1

Comments

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

Column 5 of A195978

Links

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

Formula

Empirical: a(n) = 5*a(n-1) -9*a(n-2) +11*a(n-3) -6*a(n-4) -36*a(n-5) +90*a(n-6) -142*a(n-7) +197*a(n-8) -46*a(n-9) -183*a(n-10) +478*a(n-11) -942*a(n-12) +792*a(n-13) -498*a(n-14) -210*a(n-15) +1415*a(n-16) -1639*a(n-17) +1834*a(n-18) -709*a(n-19) -862*a(n-20) +1990*a(n-21) -3015*a(n-22) +1957*a(n-23) -374*a(n-24) -1742*a(n-25) +3816*a(n-26) -3839*a(n-27) +2182*a(n-28) -480*a(n-29) -3921*a(n-30) +3721*a(n-31) -4788*a(n-32) +2840*a(n-33) +2416*a(n-34) -577*a(n-35) +7322*a(n-36) -1770*a(n-37) +1322*a(n-38) -1236*a(n-39) -6838*a(n-40) -789*a(n-41) -4538*a(n-42) -89*a(n-43) +3459*a(n-44) +1446*a(n-45) +4611*a(n-46) +1551*a(n-47) -859*a(n-48) -465*a(n-49) -2777*a(n-50) -1070*a(n-51) +363*a(n-52) -79*a(n-53) +1222*a(n-54) -43*a(n-55) -809*a(n-56) -357*a(n-57) -616*a(n-58) +368*a(n-59) +965*a(n-60) +619*a(n-61) +408*a(n-62) -203*a(n-63) -570*a(n-64) -385*a(n-65) -205*a(n-66) +35*a(n-67) +181*a(n-68) +122*a(n-69) +57*a(n-70) +5*a(n-71) -33*a(n-72) -26*a(n-73) -14*a(n-74) -8*a(n-75) -2*a(n-76)

Example

Some solutions for n=4
..1..2..2..1..2....0..0..1..1..0....0..1..1..1..2....1..1..1..0..0
..0..1..1..0..1....0..0..1..1..0....1..1..0..0..1....0..0..1..1..1
..1..1..1..0..1....1..1..1..1..0....1..1..1..1..1....1..1..1..1..1
..1..0..1..1..2....2..1..0..1..1....0..0..1..1..0....2..1..0..0..0

Crossrefs

Sequence in context: A221425 A007227 A224836 * A185918 A116015 A332373

Adjacent sequences: A195972 A195973 A195974 * A195976 A195977 A195978

Keyword

nonn

Author

R. H. Hardin Sep 25 2011

Status

approved