A299848 Number of nX4 0..1 arrays with every element equal to 0, 1, 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

8, 88, 357, 1626, 7770, 36968, 175258, 831558, 3948404, 18746665, 88997634, 422532920, 2006061193, 9524040233, 45216905030, 214675015515, 1019204087151, 4838836300654, 22973170726615, 109068876166318, 517822263781608

Offset

1,1

Comments

Column 4 of A299852.

Links

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

Formula

Empirical: a(n) = 10*a(n-1) -36*a(n-2) +90*a(n-3) -287*a(n-4) +646*a(n-5) -801*a(n-6) +1222*a(n-7) -1228*a(n-8) -1441*a(n-9) +2937*a(n-10) -8893*a(n-11) +16044*a(n-12) -4679*a(n-13) +16973*a(n-14) -8807*a(n-15) -17258*a(n-16) -36353*a(n-17) -60014*a(n-18) +68858*a(n-19) -18515*a(n-20) +379180*a(n-21) -656593*a(n-22) +1205427*a(n-23) -2227486*a(n-24) +3169065*a(n-25) -3257904*a(n-26) +3934630*a(n-27) -4581058*a(n-28) +1403565*a(n-29) -372672*a(n-30) -2494984*a(n-31) +9082223*a(n-32) -6213066*a(n-33) +9571653*a(n-34) -11974303*a(n-35) +3427023*a(n-36) -3824798*a(n-37) -5992975*a(n-38) +8720366*a(n-39) -4491961*a(n-40) +10777896*a(n-41) -2728087*a(n-42) +2084858*a(n-43) +687212*a(n-44) -5332012*a(n-45) -360422*a(n-46) -2727994*a(n-47) +497135*a(n-48) +1000057*a(n-49) +1422013*a(n-50) +462478*a(n-51) -270915*a(n-52) +3319*a(n-53) -167953*a(n-54) -158812*a(n-55) +23984*a(n-56) +38106*a(n-57) -17070*a(n-58) +11938*a(n-59) +4202*a(n-60) -5536*a(n-61) +2148*a(n-62) -472*a(n-63) +128*a(n-64) for n>66

Example

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

Crossrefs

Cf. A299852.

Sequence in context: A298191 A299085 A299341 * A299004 A299671 A299749

Adjacent sequences: A299845 A299846 A299847 * A299849 A299850 A299851

Keyword

nonn

Author

R. H. Hardin, Feb 20 2018

Status

approved