A396312 - OEIS

%I #12 May 26 2026 16:43:09

%S 1,1,1,1,5,12,22,38,72,148,301,593,1149,2242,4423,8743,17218,33815,

%T 66436,130699,257247,506154,995529,1957987,3851477,7576734,14904863,

%U 29319295,57673054,113448372,223166548,438995465,863552302,1698697632,3341519128,6573134853

%N Number of tilings of an (h+3) X n rectangle by unit squares and the Ferrers tile (h,2,2,1), for h >= 4.

%C The sequence is independent of h for h >= 4.

%H Per Alexandersson and John Ahlberg, <a href="https://arxiv.org/abs/2605.03473">Polynomials from tilings of rectangles</a>, arXiv:2605.03473 [math.CO], 2026.

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,4,3,3,6,2,2,4,0,0,1).

%F G.f.: 1/(1 - x - 4*x^4 - 3*x^5 - 3*x^6 - 6*x^7 - 2*x^8 - 2*x^9 - 4*x^10 - x^13).

%F With a(0)=1, a(n) = a(n-1) + 4*a(n-4) + 3*a(n-5) + 3*a(n-6) + 6*a(n-7) + 2*a(n-8) + 2*a(n-9) + 4*a(n-10) + a(n-13) for n >= 1.

%t CoefficientList[Series[1/(1 - x - 4*x^4 - 3*x^5 - 3*x^6 - 6*x^7 - 2*x^8 - 2*x^9 - 4*x^10 - x^13),{x,0,35}],x] (* _Stefano Spezia_, May 21 2026 *)

%Y Cf. A396311, A396313.

%K nonn,easy

%O 0,5

%A _Per Alexandersson_, May 21 2026