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A041221
Denominators of continued fraction convergents to sqrt(122).
4
1, 22, 485, 10692, 235709, 5196290, 114554089, 2525386248, 55673051545, 1227332520238, 27056988496781, 596481079449420, 13149640736384021, 289888577279897882, 6390698340894137425, 140885252076950921232, 3105866244033814404529, 68469942620820867820870
OFFSET
0,2
COMMENTS
From Michael A. Allen, May 04 2023: (Start)
Also called the 22-metallonacci sequence; the g.f. 1/(1-k*x-x^2) gives the k-metallonacci sequence.
a(n) is the number of tilings of an n-board (a board with dimensions n X 1) using unit squares and dominoes (with dimensions 2 X 1) if there are 22 kinds of squares available. (End)
LINKS
FORMULA
a(n) = F(n, 22), the n-th Fibonacci polynomial evaluated at x=22. - T. D. Noe, Jan 19 2006
From Philippe Deléham, Nov 21 2008: (Start)
a(n) = 22*a(n-1) + a(n-2) for n > 1; a(0)=1, a(1)=22.
G.f.: 1/(1 - 22*x - x^2). (End)
MATHEMATICA
Denominator[Convergents[Sqrt[122], 30]] (* Vincenzo Librandi, Dec 13 2013 *)
Fibonacci[1+Range[0, 30], 22] (* G. C. Greubel, Oct 25 2024 *)
PROG
(Magma)
[n le 2 select (22)^(n-1) else 22*Self(n-1)+Self(n-2): n in [1..31]]; // G. C. Greubel, Oct 25 2024
(SageMath)
A041221=BinaryRecurrenceSequence(22, 1, 1, 22)
[A041221(n) for n in range(31)] # G. C. Greubel, Oct 25 2024
CROSSREFS
Row n=22 of A073133, A172236 and A352361 and column k=22 of A157103.
Sequence in context: A171296 A009966 A285876 * A041926 A230350 A180780
KEYWORD
nonn,frac,easy,less,changed
EXTENSIONS
More terms from Colin Barker, Nov 14 2013
STATUS
approved