A304306 Number of nX4 0..1 arrays with every element unequal to 0, 1, 2, 3 or 5 king-move adjacent elements, with upper left element zero.

8, 65, 261, 1137, 4979, 22089, 98560, 441950, 1985853, 8936025, 40245259, 181349063, 817441187, 3685379513, 16617254516, 74932039580, 337905147089, 1523819827721, 6871941730432, 30990572266213, 139759818308246

Offset

1,1

Comments

Column 4 of A304310.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) -3*a(n-2) -12*a(n-3) -26*a(n-4) -3*a(n-5) +96*a(n-6) +29*a(n-7) +6*a(n-8) -19*a(n-9) +602*a(n-10) +260*a(n-11) -451*a(n-12) -1329*a(n-13) -2222*a(n-14) -1650*a(n-15) -4229*a(n-16) -4615*a(n-17) -5760*a(n-18) +12494*a(n-19) +28230*a(n-20) +42152*a(n-21) +30055*a(n-22) +16800*a(n-23) +11593*a(n-24) -15642*a(n-25) -80377*a(n-26) -215758*a(n-27) -220109*a(n-28) -142883*a(n-29) +45145*a(n-30) +97389*a(n-31) +272930*a(n-32) +318229*a(n-33) +310211*a(n-34) +161580*a(n-35) +30460*a(n-36) -101720*a(n-37) -220149*a(n-38) -232908*a(n-39) -139405*a(n-40) -23381*a(n-41) -9204*a(n-42) -1691*a(n-43) +13351*a(n-44) +14965*a(n-45) -2243*a(n-46) -10149*a(n-47) -6405*a(n-48) -8698*a(n-49) -12003*a(n-50) -5698*a(n-51) -606*a(n-52) -1472*a(n-53) -1446*a(n-54) -788*a(n-55) -96*a(n-56) +72*a(n-57) for n>59

Example

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

Crossrefs

Cf. A304310.

Sequence in context: A067215 A307436 A067685 * A316205 A305772 A317121

Adjacent sequences: A304303 A304304 A304305 * A304307 A304308 A304309

Keyword

nonn

Author

R. H. Hardin, May 10 2018

Status

approved