A299598 Number of nX4 0..1 arrays with every element equal to 2, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

0, 6, 27, 130, 1241, 8825, 72751, 589816, 4803248, 39358999, 321999354, 2638098994, 21610813691, 177055481680, 1450660059735, 11885674778667, 97384006706676, 797906117503448, 6537576734601907, 53565114537762363, 438881605139973564

Offset

1,2

Comments

Column 4 of A299602.

Links

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

Formula

Empirical: a(n) = 9*a(n-1) +17*a(n-2) -181*a(n-3) -358*a(n-4) +1849*a(n-5) +3395*a(n-6) -9594*a(n-7) -17373*a(n-8) +37703*a(n-9) +64155*a(n-10) -140777*a(n-11) -207284*a(n-12) +241911*a(n-13) +503248*a(n-14) -180355*a(n-15) -407315*a(n-16) +345228*a(n-17) -190109*a(n-18) -358668*a(n-19) +1352578*a(n-20) -134032*a(n-21) -796584*a(n-22) -5373391*a(n-23) +3257874*a(n-24) +6698760*a(n-25) -588489*a(n-26) -18575462*a(n-27) -9379891*a(n-28) +12753098*a(n-29) +19365970*a(n-30) +7121900*a(n-31) -19148219*a(n-32) -10185393*a(n-33) -466148*a(n-34) +6297580*a(n-35) +4336922*a(n-36) -4382384*a(n-37) +153878*a(n-38) -45486*a(n-39) -455623*a(n-40) +174413*a(n-41) -619409*a(n-42) +332546*a(n-43) +199486*a(n-44) -122028*a(n-45) +14512*a(n-46) -2012*a(n-47) +204*a(n-48)

Example

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

Crossrefs

Cf. A299602.

Sequence in context: A038176 A104745 A184279 * A343492 A323928 A360082

Adjacent sequences: A299595 A299596 A299597 * A299599 A299600 A299601

Keyword

nonn

Author

R. H. Hardin, Feb 14 2018

Status

approved