A316423 Number of nX4 0..1 arrays with every element unequal to 0, 1, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

5, 21, 32, 97, 279, 640, 1660, 4353, 10975, 28038, 72143, 184345, 471036, 1206844, 3088559, 7899309, 20219520, 51748319, 132403281, 338838244, 867145134, 2218951631, 5678392645, 14531503004, 37186210193, 95160712029, 243521427174

Offset

1,1

Comments

Column 4 of A316427.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +16*a(n-3) -24*a(n-4) -4*a(n-5) -97*a(n-6) +111*a(n-7) +33*a(n-8) +301*a(n-9) -280*a(n-10) -102*a(n-11) -610*a(n-12) +462*a(n-13) +137*a(n-14) +1003*a(n-15) -460*a(n-16) -49*a(n-17) -1229*a(n-18) +318*a(n-19) -40*a(n-20) +1076*a(n-21) -170*a(n-22) +59*a(n-23) -756*a(n-24) -85*a(n-25) -26*a(n-26) +258*a(n-27) -2*a(n-28) -278*a(n-29) -208*a(n-30) -158*a(n-31) +113*a(n-32) -92*a(n-33) +85*a(n-34) +71*a(n-35) +166*a(n-36) +46*a(n-37) -49*a(n-38) -63*a(n-39) -10*a(n-40) +6*a(n-41) +6*a(n-42) for n>43

Example

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

Crossrefs

Cf. A316427.

Sequence in context: A306168 A305645 A316921 * A317425 A074074 A006309

Adjacent sequences: A316420 A316421 A316422 * A316424 A316425 A316426

Keyword

nonn

Author

R. H. Hardin, Jul 02 2018

Status

approved