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A042861
Denominators of continued fraction convergents to sqrt(962).
3
1, 62, 3845, 238452, 14787869, 917086330, 56874140329, 3527113786728, 218737928917465, 13565278706669558, 841266017742430061, 52172058378737333340, 3235508885499457097141, 200653722959345077356082, 12443766332364894253174225, 771714166329582788774158032
OFFSET
0,2
COMMENTS
From Michael A. Allen, Jan 22 2024: (Start)
Also called the 62-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 62 kinds of squares available. (End)
LINKS
FORMULA
a(n) = F(n, 62), the n-th Fibonacci polynomial evaluated at x=62. - T. D. Noe, Jan 19 2006
From Philippe Deléham, Nov 23 2008: (Start)
a(n) = 62*a(n-1) + a(n-2), n>1; a(0)=1, a(1)=62.
G.f.: 1/(1 - 62*x - x^2). (End)
MATHEMATICA
Denominator[Convergents[Sqrt[962], 20]] (* Harvey P. Dale, Jun 15 2013 *)
CROSSREFS
Row n=62 of A073133, A172236 and A352361 and column k=62 of A157103.
Sequence in context: A206841 A206895 A207285 * A056639 A289297 A123806
KEYWORD
nonn,frac,easy
EXTENSIONS
Additional term from Colin Barker, Dec 25 2013
STATUS
approved