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 A295200 Number of nX3 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 4 1s. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified August 5 14:42 EDT 2021. Contains 346469 sequences. (Running on oeis4.)