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A296536 Number of n X 3 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 or 4 neighboring 1s. 1
1, 5, 16, 37, 96, 254, 654, 1709, 4472, 11621, 30257, 78899, 205534, 535394, 1395017, 3634476, 9468722, 24669483, 64272370, 167449745, 436262198, 1136608103, 2961236309, 7714995835, 20100110050, 52367403411, 136434332477, 355456392933 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

Empirical: a(n) = 2*a(n-1) - a(n-2) + 5*a(n-3) + a(n-4) + 6*a(n-5) + 7*a(n-6) + a(n-7) + 3*a(n-8) + 3*a(n-9) - 3*a(n-10) - 4*a(n-11) - a(n-12).

Empirical g.f.: x*(1 + 3*x + 7*x^2 + 5*x^3 + 12*x^4 + 8*x^5 + 4*x^6 + 6*x^7 - 7*x^9 - 5*x^10 - x^11) / ((1 + x^2 + x^3)*(1 - 2*x - 4*x^3 + x^4 - 2*x^5 - 4*x^6 + 3*x^8 + x^9)). - Colin Barker, Feb 23 2019

EXAMPLE

Some solutions for n=7:

..0..1..1. .1..1..0. .0..0..0. .0..1..0. .0..0..0. .0..0..1. .0..1..0

..0..1..0. .1..0..0. .1..1..0. .1..1..1. .1..1..0. .1..1..1. .1..1..1

..0..0..0. .0..0..1. .1..0..0. .0..1..0. .1..0..0. .1..0..0. .0..1..0

..1..1..0. .0..1..1. .0..0..1. .1..1..0. .0..0..0. .0..1..1. .1..1..0

..1..0..0. .0..0..0. .0..1..1. .0..0..0. .1..1..0. .0..1..0. .0..0..1

..0..1..0. .1..1..0. .0..0..0. .0..0..0. .1..0..0. .1..1..0. .1..1..1

..1..1..0. .1..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .1..0..0

CROSSREFS

Column 3 of A296541.

Sequence in context: A274248 A188427 A022496 * A041044 A042645 A218259

Adjacent sequences:  A296533 A296534 A296535 * A296537 A296538 A296539

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 15 2017

STATUS

approved

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Last modified July 4 15:43 EDT 2020. Contains 335448 sequences. (Running on oeis4.)