A295200 - OEIS

A295200

Number of nX3 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 4 1s.

1, 3, 8, 14, 25, 53, 111, 217, 426, 860, 1733, 3453, 6885, 13791, 27616, 55198, 110341, 220737, 441563, 883037, 1765930, 3532004, 7064241, 14128249, 28256121, 56512619, 113025848, 226051086, 452101185, 904203357, 1808408311, 3616815025

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OFFSET

1,2

COMMENTS

Column 3 of A295205.

LINKS

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

Robert Israel, Maple-assisted proof of formula

Index entries for linear recurrences with constant coefficients, signature(2,-1,2,1,-2)

FORMULA

Empirical: a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) +a(n-4) -2*a(n-5).

From Robert Israel, Nov 19 2017: (Start)

Empirical formula is true (see link).

G.f.: (x+x^2+3*x^3-x^4-2*x^5)/(1-2*x+x^2-2*x^3-x^4+2*x^5). (End)

EXAMPLE

Some solutions for n=7

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

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

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

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

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

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

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

MAPLE

f:= gfun:-rectoproc({a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) +a(n-4) -2*a(n-5), a(1)=1, a(2)=3, a(3)=8, a(4)=14, a(5)=25}, a(n), remember):

map(f, [$1..100]); # Robert Israel, Nov 19 2017

MATHEMATICA

LinearRecurrence[{2, -1, 2, 1, -2}, {1, 3, 8, 14, 25}, 32] (* Jean-François Alcover, Aug 27 2022 *)

CROSSREFS

Cf. A295205.

Sequence in context: A245181 A241563 A055335 * A321047 A123329 A268191

Adjacent sequences: A295197 A295198 A295199 * A295201 A295202 A295203

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 16 2017

STATUS

approved