A299085 Number of nX4 0..1 arrays with every element equal to 0, 1, 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero.

8, 88, 354, 1617, 7722, 36667, 173524, 822065, 3897261, 18474589, 87565905, 415072759, 1967506932, 9326121377, 44206712718, 209544659717, 993262158136, 4708160655145, 22317159667937, 105785574659767, 501434203894082

Offset

1,1

Comments

Column 4 of A299089.

Links

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

Formula

Empirical: a(n) = 8*a(n-1) -19*a(n-2) +43*a(n-3) -177*a(n-4) +250*a(n-5) -111*a(n-6) +598*a(n-7) +175*a(n-8) -2033*a(n-9) +835*a(n-10) -6610*a(n-11) +4604*a(n-12) +5357*a(n-13) +10181*a(n-14) +13348*a(n-15) -21106*a(n-16) -6122*a(n-17) -36475*a(n-18) +37696*a(n-19) +65360*a(n-20) +163618*a(n-21) -534123*a(n-22) +107096*a(n-23) -1235788*a(n-24) +1583118*a(n-25) +112658*a(n-26) +2520965*a(n-27) -639433*a(n-28) -3386070*a(n-29) -890603*a(n-30) -4627333*a(n-31) +6206726*a(n-32) +2036692*a(n-33) +6154747*a(n-34) +1833433*a(n-35) -4816911*a(n-36) -1469263*a(n-37) -8046242*a(n-38) +544975*a(n-39) -251241*a(n-40) +2025611*a(n-41) +2899322*a(n-42) -384613*a(n-43) +1524228*a(n-44) -1083347*a(n-45) -62502*a(n-46) -198019*a(n-47) -547484*a(n-48) +288668*a(n-49) -24160*a(n-50) +124473*a(n-51) +63988*a(n-52) -63036*a(n-53) +37665*a(n-54) -27918*a(n-55) -14368*a(n-56) +9942*a(n-57) -1736*a(n-58) -646*a(n-59) +974*a(n-60) -64*a(n-61) +264*a(n-62) -64*a(n-64) for n>66

Example

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

Crossrefs

Cf. A299089.

Sequence in context: A250228 A250276 A298191 * A299341 A299848 A299004

Adjacent sequences: A299082 A299083 A299084 * A299086 A299087 A299088

Keyword

nonn

Author

R. H. Hardin, Feb 02 2018

Status

approved