A022382 Fibonacci sequence beginning 4, 10.

4, 10, 14, 24, 38, 62, 100, 162, 262, 424, 686, 1110, 1796, 2906, 4702, 7608, 12310, 19918, 32228, 52146, 84374, 136520, 220894, 357414, 578308, 935722, 1514030, 2449752, 3963782, 6413534, 10377316, 16790850, 27168166, 43959016, 71127182, 115086198, 186213380

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

From Reeva Bohra and Greg Dresden, Aug 17 2021: (Start)

For n > 0, a(n) is the number of ways to tile, with squares and dominoes, a strip of length n+1 that begins with two vertical strips of heights 3 and 2. As an example, a(5) is the number of ways to tile this figure (of length 6) with squares and dominoes.

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(End)

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..4781
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (1,1).

Crossrefs

Cf. A001060, A022124.

Programs

Mathematica

LinearRecurrence[{1, 1}, {4, 10}, 50] (* Greg Dresden, Aug 17 2021 *)

Formula

G.f.: (4+6x)/(1-x-x^2). - Philippe Deléham, Nov 19 2008

a(n) = 2*A001060(n). - R. J. Mathar, Mar 11 2011

a(n) = Fibonacci(n+5) + Lucas(n-1). - Greg Dresden, Feb 18 2022

a(n) = a(n-1) + a(n-2). - Wesley Ivan Hurt, Mar 08 2022