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A159294
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Number of ways that a 1 X n rectangular tile T, marked into n unit squares, can be surrounded by one layer of copies of itself laid in the plane grid generated by the units of T. Ways that differ by rotation or reflection are not counted as different. The surrounded tile is the exact surrounded region.
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2
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1, 153, 301, 517, 825, 1234, 1774, 2454, 3310, 4351, 5619, 7123, 8911, 10992, 13420, 16204, 19404, 23029, 27145, 31761, 36949, 42718, 49146, 56242, 64090, 72699, 82159, 92479, 103755, 115996
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OFFSET
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1,2
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LINKS
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FORMULA
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For n>1, a(n) = (1/16)*(n^4 + 30*n^3 + 246*n^2 + 476*n + 256 + (1 if n odd, 0 if n even)*(6*n + 9)).
G.f.: -x*(63*x^7-173*x^6+15*x^5+335*x^4-228*x^3-157*x^2+150*x+1) / ((x-1)^5*(x+1)^2). - Colin Barker, Nov 26 2012
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MATHEMATICA
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Join[{1, 153}, LinearRecurrence[{3, -1, -5, 5, 1, -3, 1}, {301, 517, 825, 1234, 1774, 2454, 3310}, 49]] (* G. C. Greubel, Jun 27 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec(-x*(63*x^7-173*x^6+15*x^5 +335*x^4 -228*x^3 - 157*x^2+150*x+1)/((x-1)^5*(x+1)^2)) \\ G. C. Greubel, Jun 27 2018
(Magma) I:=[301, 517, 825, 1234, 1774, 2454, 3310]; [1, 153] cat [n le 7 select I[n] else 3*Self(n-1) -Self(n-2) -5*Self(n-3) +5*Self(n-4) + Self(n-5) -3*Self(n-6) +Self(n-7): n in [1..30]]; // G. C. Greubel, Jun 27 2018
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CROSSREFS
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Cf. A159295 for analogous problem for strip-of-hexagons tile.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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