A298829 Number of nX3 0..1 arrays with every element equal to 1, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.

0, 4, 1, 6, 10, 15, 60, 128, 267, 810, 1878, 4579, 12408, 30552, 77105, 200876, 505862, 1288511, 3311514, 8411436, 21467751, 54921524, 139947224, 357287611, 912689144, 2328342518, 5944207749, 15177139978, 38734201690, 98882999903, 252436571832

Offset

1,2

Comments

Column 3 of A298834.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +3*a(n-2) +5*a(n-3) -22*a(n-4) -15*a(n-5) +17*a(n-6) +44*a(n-7) -13*a(n-8) -49*a(n-9) +74*a(n-10) +38*a(n-11) -91*a(n-12) -61*a(n-13) +42*a(n-14) +24*a(n-15) -4*a(n-16) +a(n-17) -a(n-18) -a(n-19) for n>20

Example

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

Crossrefs

Cf. A298834.

Sequence in context: A333824 A083843 A094264 * A056140 A225419 A140895

Adjacent sequences: A298826 A298827 A298828 * A298830 A298831 A298832

Keyword

nonn

Author

R. H. Hardin, Jan 27 2018

Status

approved