cp's OEIS Frontend

A159294 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.

%I A159294 #14 Sep 08 2022 08:45:43
%S A159294 1,153,301,517,825,1234,1774,2454,3310,4351,5619,7123,8911,10992,
%T A159294 13420,16204,19404,23029,27145,31761,36949,42718,49146,56242,64090,
%U A159294 72699,82159,92479,103755,115996
%N A159294 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.
%H A159294 G. C. Greubel, <a href="/A159294/b159294.txt">Table of n, a(n) for n = 1..1000</a>
%H A159294 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-5,5,1,-3,1).
%F A159294 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)).
%F A159294 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
%t A159294 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 *)
%o A159294 (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
%o A159294 (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
%Y A159294 Cf. A159295 for analogous problem for strip-of-hexagons tile.
%K A159294 nonn,easy
%O A159294 1,2
%A A159294 _David Pasino_, Apr 09 2009