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A296798
Number of n X 2 0..1 arrays with each 1 adjacent to 1, 3 or 4 king-move neighboring 1s.
1
2, 8, 15, 41, 122, 308, 855, 2405, 6522, 18080, 50223, 138353, 383114, 1061116, 2933431, 8119437, 22473514, 62177224, 172075759, 476212281, 1317772378, 3646788996, 10092010711, 27927735285, 77286019354, 213877500592
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = a(n-1) + 3*a(n-2) + 9*a(n-3) - 4*a(n-4) - 12*a(n-5) - 16*a(n-6).
Empirical g.f.: x*(1 + 2*x)*(2 + 2*x - 3*x^2 - 10*x^3 - 8*x^4) / ((1 - x^2 - 2*x^3)*(1 - x - 2*x^2 - 8*x^3)). - Colin Barker, Feb 25 2019
EXAMPLE
Some solutions for n=7:
..1..1. .1..0. .1..0. .0..0. .1..1. .0..0. .0..1. .1..0. .0..0. .0..0
..0..0. .1..0. .0..1. .1..0. .1..1. .0..0. .1..0. .1..0. .1..1. .1..0
..1..1. .0..0. .0..0. .0..1. .0..0. .1..0. .0..0. .1..1. .0..0. .0..1
..1..1. .1..1. .1..1. .1..1. .1..1. .0..1. .1..0. .1..1. .1..0. .0..0
..0..1. .1..1. .0..0. .1..1. .0..0. .0..0. .1..0. .0..0. .0..1. .0..0
..0..1. .0..1. .0..1. .0..1. .0..1. .0..1. .0..0. .1..0. .1..1. .0..1
..0..0. .0..1. .0..1. .0..1. .1..0. .0..1. .0..0. .1..0. .1..1. .0..1
CROSSREFS
Column 2 of A296804.
Sequence in context: A082638 A077388 A301986 * A203419 A173287 A167592
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 20 2017
STATUS
approved