cp's OEIS Frontend

A385633 a(n) = a(n-1) + a(n-3), with a(0) = 1, a(1) = 4, a(2) = 8.

%I A385633 #15 Jul 09 2025 22:14:59
%S A385633 1,4,8,9,13,21,30,43,64,94,137,201,295,432,633,928,1360,1993,2921,
%T A385633 4281,6274,9195,13476,19750,28945,42421,62171,91116,133537,195708,
%U A385633 286824,420361,616069,902893,1323254,1939323,2842216,4165470,6104793,8947009,13112479,19217272
%N A385633 a(n) = a(n-1) + a(n-3), with a(0) = 1, a(1) = 4, a(2) = 8.
%C A385633 a(n) is the number of ways to tile this shape, of length n, with 1 X 1 squares and 1 X 3 rectangles (which can be either horizontal or vertical).
%C A385633     _
%C A385633    |_|_
%C A385633    |_|_|______________
%C A385633    |_|_|_|_|_|_|_|_|_|
%C A385633    |_|_|
%C A385633    |_|
%H A385633 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1).
%F A385633 a(n) = b(n+4) + 2*b(n-5) for b(n) = A000930(n), Narayana's cows sequence.
%F A385633 G.f.: (1 + 3*x + 4*x^2)/(1 - x - x^3). - _Stefano Spezia_, Jul 06 2025
%e A385633 Shown here is one of the a(4)=13 ways to tile this shape of length 4:
%e A385633    _
%e A385633   | |_
%e A385633   | | |____
%e A385633   |_| |_|_|
%e A385633   |_|_|
%e A385633   |_|
%t A385633 LinearRecurrence[{1, 0, 1}, {1, 4, 8}, 40]
%Y A385633 Cf. A000930, A179070.
%K A385633 nonn,easy
%O A385633 0,2
%A A385633 _Greg Dresden_ and Saim Usmani, Jul 05 2025