A022138 Fibonacci sequence beginning 5, 13.

5, 13, 18, 31, 49, 80, 129, 209, 338, 547, 885, 1432, 2317, 3749, 6066, 9815, 15881, 25696, 41577, 67273, 108850, 176123, 284973, 461096, 746069, 1207165, 1953234, 3160399, 5113633, 8274032, 13387665, 21661697, 35049362, 56711059, 91760421, 148471480

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

From Greg Dresden and Wajdi Maaloul, Jun 19 2022: (Start)

a(n) is the number of ways to tile this strip of length n+4 (with a bump in the n=5 position) using squares and dominos.

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(End)

Links

• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (1,1).

Crossrefs

Cf. A000032, A000045.

Programs

Mathematica

LinearRecurrence[{1, 1}, {5, 13}, 50] (* Harvey P. Dale, Jul 10 2017 *)
CoefficientList[Series[(5 + 8x)/(1 - x - x^2), {x, 0, 50}], x] (* Stefano Spezia, Oct 11 2018 *)

Formula

a(0) = 5, a(1) = 13, a(n) = a(n - 2) + a(n - 1).

G.f.: (5 + 8x)/(1 - x - x^2). - Philippe Deléham, Nov 20 2008

E.g.f.: exp(x/2)*(25*cosh(sqrt(5)*x/2) + 21*sqrt(5)*sinh(sqrt(5)*x/2))/5. - Stefano Spezia, Jun 06 2023