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A041265
Denominators of continued fraction convergents to sqrt(145).
3
1, 24, 577, 13872, 333505, 8017992, 192765313, 4634385504, 111418017409, 2678666803320, 64399421297089, 1548264777933456, 37222754091700033, 894894362978734248, 21514687465581321985, 517247393536930461888, 12435452132351912407297
OFFSET
0,2
COMMENTS
From Michael A. Allen, May 04 2023: (Start)
Also called the 24-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 24 kinds of squares available. (End)
LINKS
FORMULA
a(n) = F(n, 24), the n-th Fibonacci polynomial evaluated at x=24. - T. D. Noe, Jan 19 2006
From Philippe Deléham, Nov 21 2008: (Start)
a(n) = 24*a(n-1) + a(n-2) for n > 1, a(0)=1, a(1)=24.
G.f.: 1/(1-24*x-x^2). (End)
MATHEMATICA
Denominator[Convergents[Sqrt[145], 30]] (* Vincenzo Librandi, Dec 14 2013 *)
CROSSREFS
Row n=24 of A073133, A172236 and A352361 and column k=24 of A157103.
Sequence in context: A171298 A268027 A009968 * A042106 A158637 A179059
KEYWORD
nonn,frac,easy,less
EXTENSIONS
More terms from Colin Barker, Nov 14 2013
STATUS
approved