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A185691
Fibonacci sequence with initial terms 10 and 21.
1
10, 21, 31, 52, 83, 135, 218, 353, 571, 924, 1495, 2419, 3914, 6333, 10247, 16580, 26827, 43407, 70234, 113641, 183875, 297516, 481391, 778907, 1260298, 2039205, 3299503, 5338708, 8638211, 13976919, 22615130, 36592049, 59207179, 95799228
OFFSET
0,1
COMMENTS
From Wajdi Maaloul, Jun 23 2022: (Start)
For n>0, a(n) is the number of ways to tile the figure below with squares and dominoes (a strip of length n+2 that contains two vertical strip of height 3 in its first and third tiles).
_ _
|_| |_|
|_|_|_|_____ _
|_|_|_|_|_|_|...|_|
(End)
FORMULA
From G. C. Greubel, Jul 10 2017: (Start)
a(n+2) = a(n+1) + a(n) with a(0) = 10, a(1) = 21.
a(n) = 11*Fibonacci(n) + 10*Fibonacci(n+1).
a(n) = 9*Fibonacci(n+2) + Lucas(n+1).
G.f.: (10 + 11*x)/(1 - x - x^2).
E.g.f.: (1/sqrt(5))*exp(x/2)*(32*sinh(sqrt(5)*x/2) + 10*sqrt(5)*cosh(sqrt(5)*x/2)). (End)
MATHEMATICA
Join[{a=10, b=21}, Table[c=a+b; a=b; b=c, {n, 60}]]
CoefficientList[Series[(10 + 11*x)/(1 - x - x^2), {x, 0, 50}], x] (* G. C. Greubel, Jul 10 2017 *)
LinearRecurrence[{1, 1}, {10, 21}, 40] (* Harvey P. Dale, Aug 01 2024 *)
PROG
(PARI) x='x+O('x^50); Vec((10 + 11*x)/(1 - x - x^2)) \\ G. C. Greubel, Jul 10 2017
CROSSREFS
Sequence in context: A245071 A256825 A190326 * A042291 A041194 A042871
KEYWORD
nonn
AUTHOR
STATUS
approved