A317039 Number of nX4 0..1 arrays with every element unequal to 0, 1, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

5, 21, 33, 141, 610, 2516, 14294, 88030, 509381, 3093005, 19312237, 118337189, 727121421, 4504400841, 27814686154, 171570763044, 1060312932793, 6551216623239, 40456288742814, 249917071426582, 1543961418215996

Offset

1,1

Comments

Column 4 of A317043.

Links

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

Formula

Empirical: a(n) = 12*a(n-1) -53*a(n-2) +212*a(n-3) -1067*a(n-4) +3283*a(n-5) -7149*a(n-6) +22550*a(n-7) -60499*a(n-8) +111428*a(n-9) -255645*a(n-10) +566156*a(n-11) -963436*a(n-12) +1783859*a(n-13) -2972693*a(n-14) +4666054*a(n-15) -7467897*a(n-16) +8654259*a(n-17) -12205787*a(n-18) +15382900*a(n-19) -8013589*a(n-20) +9971092*a(n-21) +4366120*a(n-22) -38850043*a(n-23) +48297824*a(n-24) -95813499*a(n-25) +154140740*a(n-26) -222888798*a(n-27) +265742479*a(n-28) -255691820*a(n-29) +399479858*a(n-30) -401654404*a(n-31) +385831534*a(n-32) -397757831*a(n-33) +67971892*a(n-34) -270794607*a(n-35) +350468437*a(n-36) +255979054*a(n-37) -209173625*a(n-38) +190177950*a(n-39) -222665052*a(n-40) -131151071*a(n-41) -55961197*a(n-42) -133828132*a(n-43) +99648586*a(n-44) +97475736*a(n-45) +30041612*a(n-46) +11310024*a(n-47) +1563480*a(n-48) -480320*a(n-49) -244512*a(n-50) +74432*a(n-51) +12032*a(n-52) for n>55

Example

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

Crossrefs

Cf. A317043.

Sequence in context: A074074 A006309 A273577 * A317693 A145026 A039561

Adjacent sequences: A317036 A317037 A317038 * A317040 A317041 A317042

Keyword

nonn

Author

R. H. Hardin, Jul 19 2018

Status

approved