A296684 Number of nX4 0..1 arrays with each 1 adjacent to 1, 2 or 3 king-move neighboring 1s.

7, 145, 1162, 11478, 121477, 1210458, 12227803, 124103052, 1254382781, 12689916581, 128420744670, 1299239741961, 13145213613487, 133001572025151, 1345666857760526, 13615069768087393, 137753603402933018

Offset

1,1

Comments

Column 4 of A296688.

Links

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

Robert Israel, Maple-assisted proof of formula

Formula

Empirical: a(n) = 7*a(n-1) +15*a(n-2) +181*a(n-3) -141*a(n-4) +269*a(n-5) -2149*a(n-6) -2006*a(n-7) -3785*a(n-8) -973*a(n-9) +8803*a(n-10) +516*a(n-11) -2504*a(n-12) +3529*a(n-13) -5347*a(n-14) +1719*a(n-15) +3063*a(n-16) -2485*a(n-17) -404*a(n-18) -697*a(n-19) +572*a(n-20) +47*a(n-21) +143*a(n-22) +82*a(n-23) -100*a(n-24) -10*a(n-25) +4*a(n-26).

Empirical formula confirmed by Robert Israel, Dec 18 2017: see link.

Example

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

Crossrefs

Cf. A296688.

Sequence in context: A156978 A163028 A367527 * A012826 A232363 A102059

Adjacent sequences: A296681 A296682 A296683 * A296685 A296686 A296687

Keyword

nonn

Author

R. H. Hardin, Dec 18 2017

Status

approved