A197675 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,0,1 for x=0,1,2,3,4

5, 33, 202, 1111, 5639, 29190, 153715, 817865, 4363976, 23310791, 124634939, 666885018, 3570183285, 19119296745, 102409115514, 548602179057, 2939069643391, 15746490425394, 84366772518821, 452030585522887

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

Column 4 of A197679

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 6*a(n-1) +a(n-2) -13*a(n-3) -42*a(n-4) -42*a(n-5) -195*a(n-6) -185*a(n-7) -610*a(n-8) +1669*a(n-9) +6927*a(n-10) +10455*a(n-11) +17106*a(n-12) +6763*a(n-13) -7146*a(n-14) -61192*a(n-15) -137955*a(n-16) -233080*a(n-17) -251923*a(n-18) -85264*a(n-19) +188050*a(n-20) +738784*a(n-21) +961941*a(n-22) +1054061*a(n-23) +412812*a(n-24) -514393*a(n-25) -1366895*a(n-26) -1838621*a(n-27) -965534*a(n-28) -217508*a(n-29) +650476*a(n-30) +663462*a(n-31) +297533*a(n-32) +407331*a(n-33) +536238*a(n-34) +566597*a(n-35) +117114*a(n-36) -598606*a(n-37) -567790*a(n-38) -431633*a(n-39) +303180*a(n-40) +313530*a(n-41) +378270*a(n-42) -10198*a(n-43) -117707*a(n-44) -270167*a(n-45) -193155*a(n-46) -148612*a(n-47) -44050*a(n-48) +18464*a(n-49) +79364*a(n-50) +78108*a(n-51) +61809*a(n-52) +29990*a(n-53) +7690*a(n-54) -3729*a(n-55) -2340*a(n-56) +2200*a(n-57) +4364*a(n-58) +4100*a(n-59) +2297*a(n-60) +662*a(n-61) -257*a(n-62) -456*a(n-63) -421*a(n-64) -227*a(n-65) -86*a(n-66) -16*a(n-67) -a(n-68) for n>69

Example

Some solutions containing all values 0 to 4 for n=5
..2..1..0..0....1..0..0..0....0..0..0..1....0..3..0..0....1..0..1..2
..1..4..1..1....1..0..3..0....0..3..0..1....0..0..3..0....2..1..4..1
..0..1..1..1....2..1..1..0....0..1..1..2....1..1..1..0....2..1..1..0
..0..3..0..0....2..1..4..1....1..4..1..2....1..1..4..1....1..0..3..0
..0..0..0..0....1..0..1..2....2..1..0..1....0..0..1..2....1..0..0..0

Crossrefs

Sequence in context: A050915 A091056 A244901 * A015544 A155597 A250163

Adjacent sequences: A197672 A197673 A197674 * A197676 A197677 A197678

Keyword

nonn

Author

R. H. Hardin Oct 17 2011

Status

approved