

A296821


Number of n X 2 0..1 arrays with each 1 adjacent to 2, 3 or 4 kingmove neighboring 1s.


1



1, 6, 21, 56, 178, 609, 1997, 6511, 21494, 71021, 234110, 771936, 2546839, 8401997, 27715289, 91426922, 301604833, 994943072, 3282138566, 10827217153, 35717165621, 117824839843, 388684058778, 1282202639897, 4229768507606
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OFFSET

1,2


LINKS

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


FORMULA

Empirical: a(n) = 3*a(n1) + 5*a(n3)  2*a(n4)  10*a(n5)  8*a(n6).
Empirical g.f.: x*(1 + 3*x + 3*x^2  12*x^3  18*x^4  8*x^5) / (1  3*x  5*x^3 + 2*x^4 + 10*x^5 + 8*x^6).  Colin Barker, Feb 25 2019


EXAMPLE

Some solutions for n=7:
..1..1. .0..0. .1..1. .1..1. .1..0. .1..1. .1..1. .0..1. .1..0. .0..1
..1..0. .0..0. .0..1. .1..0. .1..1. .1..0. .0..1. .1..1. .1..1. .1..1
..1..0. .0..0. .1..1. .0..0. .1..0. .1..1. .1..1. .0..1. .0..1. .0..0
..1..0. .0..0. .0..0. .0..0. .1..1. .1..0. .0..1. .0..0. .0..0. .0..0
..1..0. .1..0. .1..1. .1..0. .1..1. .0..0. .1..1. .1..1. .0..1. .1..0
..0..1. .1..1. .1..1. .1..1. .0..0. .0..1. .0..0. .0..1. .1..1. .1..1
..1..1. .0..0. .0..1. .1..1. .0..0. .1..1. .0..0. .1..1. .0..0. .0..1


CROSSREFS

Column 2 of A296827.
Sequence in context: A256571 A247904 A074745 * A056414 A056341 A144899
Adjacent sequences: A296818 A296819 A296820 * A296822 A296823 A296824


KEYWORD

nonn


AUTHOR

R. H. Hardin, Dec 21 2017


STATUS

approved



