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A022138
Fibonacci sequence beginning 5, 13.
3
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
0,1
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.
. _
._______|_|_________ _
|_|_|_|_|_|_|_|_|_|_|...|_|
(End)
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
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 *)
CROSSREFS
Sequence in context: A101864 A190432 A197563 * A226193 A028274 A272723
KEYWORD
nonn,easy
STATUS
approved