A299678 Number of nX4 0..1 arrays with every element equal to 0, 1, 2, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

8, 29, 45, 211, 1477, 7279, 35408, 196107, 1040287, 5315858, 28124011, 149025299, 777448355, 4081354892, 21511416831, 112879169620, 592476764652, 3115326159997, 16366236764640, 85947859462952, 451603410329806

Offset

1,1

Comments

Column 4 of A299682.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) -6*a(n-2) +56*a(n-3) -243*a(n-4) +21*a(n-5) -437*a(n-6) +3223*a(n-7) -4595*a(n-8) +10082*a(n-9) -21139*a(n-10) +50558*a(n-11) -135270*a(n-12) +248619*a(n-13) -324967*a(n-14) +491379*a(n-15) -1145574*a(n-16) +1798776*a(n-17) -2438838*a(n-18) +3186250*a(n-19) -3751124*a(n-20) +4785763*a(n-21) -4984892*a(n-22) +5983608*a(n-23) -4269978*a(n-24) +4011088*a(n-25) -6338505*a(n-26) +5444651*a(n-27) -7492403*a(n-28) +5780137*a(n-29) -9099704*a(n-30) +4564720*a(n-31) -3039734*a(n-32) -808886*a(n-33) +12731179*a(n-34) -19207932*a(n-35) +30963112*a(n-36) -19704562*a(n-37) +20972375*a(n-38) -10591705*a(n-39) +875475*a(n-40) +7526951*a(n-41) -12820425*a(n-42) +6206261*a(n-43) -11152799*a(n-44) -1704733*a(n-45) +879253*a(n-46) -4852078*a(n-47) +2300159*a(n-48) +195288*a(n-49) +1765994*a(n-50) +1922313*a(n-51) +480549*a(n-52) -84268*a(n-53) -435326*a(n-54) -156870*a(n-55) -26140*a(n-56) +10628*a(n-57) +9372*a(n-58) +1280*a(n-59) +424*a(n-60) +48*a(n-61) for n>64

Example

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

Crossrefs

Cf. A299682.

Sequence in context: A034167 A299011 A299802 * A300310 A171442 A341402

Adjacent sequences: A299675 A299676 A299677 * A299679 A299680 A299681

Keyword

nonn

Author

R. H. Hardin, Feb 16 2018

Status

approved