A316921 Number of nX4 0..1 arrays with every element unequal to 0, 1, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

5, 21, 31, 137, 594, 2574, 15118, 95244, 569635, 3550989, 22664602, 142267931, 895070740, 5670787406, 35824811579, 226112280654, 1429458076391, 9034826810108, 57079202265029, 360713789484186, 2279666370535566

Offset

1,1

Comments

Column 4 of A316925.

Links

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

Formula

Empirical: a(n) = 12*a(n-1) -51*a(n-2) +195*a(n-3) -1005*a(n-4) +2944*a(n-5) -5362*a(n-6) +17291*a(n-7) -47505*a(n-8) +74205*a(n-9) -168436*a(n-10) +362058*a(n-11) -413187*a(n-12) +663946*a(n-13) -969737*a(n-14) +420286*a(n-15) -481243*a(n-16) +147478*a(n-17) +1080505*a(n-18) -2336922*a(n-19) +6600322*a(n-20) -6551295*a(n-21) +4173168*a(n-22) -688068*a(n-23) +7432137*a(n-24) -12589162*a(n-25) -9372774*a(n-26) -10500723*a(n-27) +7447976*a(n-28) -25119541*a(n-29) +41488482*a(n-30) +73870327*a(n-31) +55330350*a(n-32) -120181727*a(n-33) -118352377*a(n-34) +7630520*a(n-35) +110429964*a(n-36) +53450039*a(n-37) -34148921*a(n-38) -41621802*a(n-39) -10964908*a(n-40) +11985455*a(n-41) +6354761*a(n-42) -2636376*a(n-43) -2126588*a(n-44) -231100*a(n-45) +594984*a(n-46) +139724*a(n-47) -101338*a(n-48) -11668*a(n-49) +9336*a(n-50) +1440*a(n-51) for n>55

Example

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

Crossrefs

Cf. A316925.

Sequence in context: A304665 A306168 A305645 * A316423 A317425 A074074

Adjacent sequences: A316918 A316919 A316920 * A316922 A316923 A316924

Keyword

nonn

Author

R. H. Hardin, Jul 16 2018

Status

approved