A111572 - OEIS

A111572

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

-1, 3, 2, 1, 3, 8, 11, 15, 26, 45, 71, 112, 183, 299, 482, 777, 1259, 2040, 3299, 5335, 8634, 13973, 22607, 36576, 59183, 95763, 154946, 250705, 405651, 656360, 1062011, 1718367, 2780378, 4498749, 7279127, 11777872, 19056999, 30834875, 49891874, 80726745

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OFFSET

0,2

COMMENTS

See comment and FAMP code for A111569.

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

From Greg Dresden and Jiaqi Wang, Jun 24 2023: (Start)

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:

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LINKS

Table of n, a(n) for n=0..39.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 1, 1).

FORMULA

G.f.: (1-4*x+x^2)/((1+x^2)*(x^2+x-1))

From Greg Dresden and Jiaqi Wang, Jun 24 2023: (Start)

a(2*n) = F(n+1)*L(n-1) + F(n)*F(n-1),

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.

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