A183452 Number of n X 5 binary arrays with every 1 having exactly three king-move neighbors equal to 1.

1, 6, 13, 22, 60, 147, 310, 723, 1723, 3917, 8973, 20875, 48427, 111384, 256857, 599340, 1384994, 3187563, 7469888, 17334233, 39905291, 94076289, 219435873, 505824167, 1202595689, 2825927772, 6530389759, 15704159500, 37297212976

Offset

1,2

Comments

Column 5 of A183456.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Conjecture: g.f. -x*(1 +5*x +607360*x^20 -11532*x^9 +753306*x^19 +6*x^2 -288*x^26 -57080*x^10 -612804*x^16 +7234*x^8 -600857*x^17 +181998*x^18 -57*x^3 -10592*x^25 -16800*x^24 -182104*x^23 -283*x^4 +5942*x^7 -132231*x^15 -345*x^5 +1200*x^6+ 285093*x^14 +259034*x^13 +52803*x^12 +384*x^29 +768*x^28 +2048*x^27 -67623*x^11 -344072*x^22 -99176*x^21)/(-1 +x +275562*x^20 +15867*x^9 -37876*x^19 +x^2 -8768*x^26 +384*x^30 -7896*x^10 -20075*x^16 +1261*x^8 -184239*x^17 -567185*x^18 +60*x^3 -8096*x^25 -174456*x^24 -168944*x^23 -52*x^4+980*x^7 +311194*x^15-58*x^5 -1393*x^6 +65529*x^14 +24304*x^13 -94858*x^12 +384*x^29 +1664*x^28 -1952*x^27 -12862*x^11 +73800*x^22 +537480*x^21) . - R. J. Mathar, Dec 03 2022

Example

Some solutions for 7X5
..0..0..0..1..1....0..0..0..1..1....0..0..0..0..0....0..0..0..0..0
..1..1..0..1..1....0..0..0..1..1....0..1..1..0..0....0..0..0..0..0
..1..1..0..0..0....0..0..0..0..0....0..1..1..0..0....1..1..0..0..0
..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....1..1..0..1..1
..0..0..0..0..0....0..0..0..0..0....1..1..0..0..0....0..0..0..1..1
..1..1..0..1..1....0..0..0..1..1....1..1..0..1..1....1..1..0..0..0
..1..1..0..1..1....0..0..0..1..1....0..0..0..1..1....1..1..0..0..0

Crossrefs

Sequence in context: A049718 A036707 A054311 * A323423 A236577 A356091

Adjacent sequences: A183449 A183450 A183451 * A183453 A183454 A183455

Keyword

nonn

Author

R. H. Hardin, Jan 05 2011

Status

approved