cp's OEIS Frontend

A111572 a(n) = a(n-1) + a(n-3) + a(n-4), n >= 4, with initial terms -1,3,2,1.

%I A111572 #26 Feb 07 2025 00:35:01
%S A111572 -1,3,2,1,3,8,11,15,26,45,71,112,183,299,482,777,1259,2040,3299,5335,
%T A111572 8634,13973,22607,36576,59183,95763,154946,250705,405651,656360,
%U A111572 1062011,1718367,2780378,4498749,7279127,11777872,19056999,30834875,49891874,80726745
%N A111572 a(n) = a(n-1) + a(n-3) + a(n-4), n >= 4, with initial terms -1,3,2,1.
%C A111572 See comment and FAMP code for A111569.
%C A111572 Floretion Algebra Multiplication Program, FAMP Code: 4ibaseseq[B+H] with B = - .25'i + .25'j - .25i' + .25j' + k' - .5'kk' - .25'ik' - .25'jk' - .25'ki' - .25'kj' - .5e and H = + .75'ii' + .75'jj' + .75'kk' + .75e
%C A111572 From _Greg Dresden_ and Jiaqi Wang, Jun 24 2023: (Start)
%C A111572 For n >= 5, a(n) is also the number of ways to tile this "central staircase" figure of length n-2 with squares and dominoes. This is the picture for length 9; there are a(11)=112 ways to tile it:
%C A111572              _
%C A111572    _________|_|_____
%C A111572   |_|_|_|_|_|_|_|_|_|
%C A111572         |_|            (End)
%H A111572 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 1, 1).
%F A111572 G.f.: (1-4*x+x^2)/((1+x^2)*(x^2+x-1))
%F A111572 From _Greg Dresden_ and Jiaqi Wang, Jun 24 2023: (Start)
%F A111572 a(2*n) = F(n+1)*L(n-1) + F(n)*F(n-1),
%F A111572 a(2*n+1) = F(n+1)*(F(n+1) + 2*F(n-1)), for F(n) and L(n) the Fibonacci and Lucas numbers.
%F A111572 (End)
%Y A111572 Cf. A001638, A111569, A111570, A111571, A111573, A111574, A111575, A111576.
%Y A111572 Cf. A000032, A000045.
%K A111572 easy,sign
%O A111572 0,2
%A A111572 _Creighton Dement_, Aug 10 2005
%E A111572 Name clarified by _Robert C. Lyons_, Feb 06 2025