A316214 Number of nX4 0..1 arrays with every element unequal to 0, 1, 2, 4, 5 or 8 king-move adjacent elements, with upper left element zero.

8, 28, 75, 310, 1468, 5883, 25093, 108869, 463940, 1986171, 8536518, 36607272, 157097926, 674669588, 2896563138, 12438785892, 53424623277, 229451570948, 985550702393, 4233369125303, 18184230957117, 78112038108544

Offset

1,1

Comments

Column 4 of A316218.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) +8*a(n-2) +28*a(n-3) -230*a(n-4) -368*a(n-5) +53*a(n-6) +5088*a(n-7) +6781*a(n-8) -7976*a(n-9) -60908*a(n-10) -66351*a(n-11) +103837*a(n-12) +442491*a(n-13) +387636*a(n-14) -667285*a(n-15) -2056660*a(n-16) -1451166*a(n-17) +2561215*a(n-18) +6311455*a(n-19) +3649829*a(n-20) -6267637*a(n-21) -13045989*a(n-22) -6577356*a(n-23) +9820868*a(n-24) +18639683*a(n-25) +9680153*a(n-26) -9136360*a(n-27) -19752012*a(n-28) -13530671*a(n-29) +3507009*a(n-30) +18236801*a(n-31) +17732691*a(n-32) +1569127*a(n-33) -17775199*a(n-34) -18568764*a(n-35) -1027489*a(n-36) +17236131*a(n-37) +13166391*a(n-38) -2749309*a(n-39) -12863222*a(n-40) -5219279*a(n-41) +4257952*a(n-42) +6203936*a(n-43) +472740*a(n-44) -2775913*a(n-45) -1690310*a(n-46) +482298*a(n-47) +981255*a(n-48) +129709*a(n-49) -211889*a(n-50) -179738*a(n-51) +59067*a(n-52) +34821*a(n-53) -4096*a(n-54) -4723*a(n-55) -4638*a(n-56) +5416*a(n-57) +782*a(n-58) -676*a(n-59) -240*a(n-60) -64*a(n-61) +48*a(n-62) for n>64

Example

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

Crossrefs

Cf. A316218.

Sequence in context: A102665 A212565 A209408 * A134638 A293289 A305638

Adjacent sequences: A316211 A316212 A316213 * A316215 A316216 A316217

Keyword

nonn

Author

R. H. Hardin, Jun 26 2018

Status

approved