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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 (list; graph; refs; listen; history; text; internal format)
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*x-1) / ((x-1)^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*x-1)/( (x-1)^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(n-1) -3*Self(n-2) -8*Self(n-3) +14*Self(n-4) -14*Self(n-6) +8*Self(n-7) +3*Self(n-8) -4*Self(n-9) +Self(n-10): n in [1..30]]; // G. C. Greubel, Jun 27 2018

CROSSREFS

Cf. A159294 for analogous problem for strip-of-squares 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

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Last modified December 6 14:15 EST 2019. Contains 329806 sequences. (Running on oeis4.)