A196908 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,1,2,0,4 for x=0,1,2,3,4

4, 34, 193, 1193, 7290, 45491, 280860, 1735427, 10739750, 66445820, 411015542, 2542717000, 15730689695, 97316972504, 602047008407, 3724552586585, 23041857722486, 142547865080477, 881869011688921, 5455662175125561

Offset

1,1

Comments

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

Column 4 of A196912

Links

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

Formula

Empirical: a(n) = 4*a(n-1) +7*a(n-2) +51*a(n-3) -8*a(n-4) -234*a(n-5) -550*a(n-6) -1005*a(n-7) -754*a(n-8) -4639*a(n-9) -15431*a(n-10) -4702*a(n-11) +56095*a(n-12) +101261*a(n-13) +18623*a(n-14) -181520*a(n-15) -161109*a(n-16) +176367*a(n-17) +223379*a(n-18) -192522*a(n-19) -366850*a(n-20) +78186*a(n-21) +422433*a(n-22) +62433*a(n-23) -238648*a(n-24) -110038*a(n-25) +144587*a(n-26) +321508*a(n-27) -209413*a(n-28) -370198*a(n-29) +225119*a(n-30) +126855*a(n-31) -59298*a(n-32) -62721*a(n-33) -106880*a(n-34) +108464*a(n-35) +106059*a(n-36) -74019*a(n-37) -53062*a(n-38) +33772*a(n-39) +20046*a(n-40) -13761*a(n-41) -2034*a(n-42) +1285*a(n-43) -168*a(n-44) -534*a(n-45) +503*a(n-46) +382*a(n-47) -326*a(n-48) +97*a(n-49) -40*a(n-50) +11*a(n-51) +a(n-52) -4*a(n-53) +3*a(n-54) -a(n-55)

Example

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

Crossrefs

Sequence in context: A297715 A129557 A231518 * A197075 A085695 A049293

Adjacent sequences: A196905 A196906 A196907 * A196909 A196910 A196911

Keyword

nonn

Author

R. H. Hardin Oct 07 2011

Status

approved