

A159295


Number of ways that a tile in the form of a strip of n congruent regular hexagons stuck together on successive parallel edges can be surrounded by one layer of copies of itself in a plane. Ways that differ by rotation or reflection are not counted as different. The surrounded tile is the exact surrounded region.


2



1, 721, 1842, 4025, 7856, 14124, 23936, 38654, 60090, 90407, 132374, 189223, 264972, 364230, 492596, 656404, 863206, 1121449, 1441050, 1832997, 2310024, 2886128, 3577352, 4401210, 5377586, 6528059, 7876926, 9450419, 11277860
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OFFSET

1,2


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (4,3,8,14,0,14,8,3,4,1).


FORMULA

a(1) = 1, a(2) = 721, and if n > 2 then a(n) = (1/144)*(n^6 + 30*n^5 + 463*n^4 + 3132*n^3 + 11506*n^2 + 10716*n  1152 + (n odd)(9*n^2 + 90*n + 261)).
G.f.: x*(28*x^11 285*x^10 +784*x^9 307*x^8 1866*x^7 +2566*x^6 +583*x^5 3036*x^4 +1172*x^3 +1039*x^2 717*x1) / ((x1)^7*(x+1)^3).  Colin Barker, Nov 26 2012


MATHEMATICA

Join[{1, 721}, LinearRecurrence[{4, 3, 8, 14, 0, 14, 8, 3, 4, 1}, {1842, 4025, 7856, 14124, 23936, 38654, 60090, 90407, 132374, 189223}, 30]] (* Harvey P. Dale, Dec 04 2014 *)


PROG

(PARI) x='x+O('x^30); Vec(x*(28*x^11 285*x^10 +784*x^9 307*x^8 1866*x^7 +2566*x^6 +583*x^5 3036*x^4 +1172*x^3 +1039*x^2 717*x1)/( (x1)^7*(x+1)^3)) \\ G. C. Greubel, Jun 27 2018
(MAGMA) I:=[1842, 4025, 7856, 14124, 23936, 38654, 60090, 90407, 132374, 189223]; [1, 721] cat [n le 10 select I[n] else 4*Self(n1) 3*Self(n2) 8*Self(n3) +14*Self(n4) 14*Self(n6) +8*Self(n7) +3*Self(n8) 4*Self(n9) +Self(n10): n in [1..30]]; // G. C. Greubel, Jun 27 2018


CROSSREFS

Cf. A159294 for analogous problem for stripofsquares tile.
Sequence in context: A119452 A034179 A014440 * A154515 A241961 A318527
Adjacent sequences: A159292 A159293 A159294 * A159296 A159297 A159298


KEYWORD

nonn,easy


AUTHOR

David Pasino, Apr 09 2009


EXTENSIONS

Typo in formula corrected by David Pasino, Apr 15 2009


STATUS

approved



