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A041481
Denominators of continued fraction convergents to sqrt(257).
3
1, 32, 1025, 32832, 1051649, 33685600, 1078990849, 34561392768, 1107043559425, 35459955294368, 1135825612979201, 36381879570628800, 1165355971873100801, 37327772979509854432, 1195654091316188442625, 38298258695097540018432, 1226739932334437469032449
OFFSET
0,2
COMMENTS
From Michael A. Allen, May 16 2023: (Start)
Also called the 32-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 32 kinds of squares available. (End)
LINKS
FORMULA
a(n) = F(n, 32), the n-th Fibonacci polynomial evaluated at x=32. - T. D. Noe, Jan 19 2006
a(n) = 32*a(n-1)+a(n-2) for n>1; a(0)=1, a(1)=32. G.f.: 1/(1-32*x-x^2). [Philippe Deléham, Nov 23 2008]
MATHEMATICA
a=0; lst={}; s=0; Do[a=s-(a-1); AppendTo[lst, a]; s+=a*32, {n, 3*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 27 2009 *)
Denominator[Convergents[Sqrt[257], 30]] (* Vincenzo Librandi, Dec 18 2013 *)
LinearRecurrence[{32, 1}, {1, 32}, 30] (* Harvey P. Dale, Nov 03 2015 *)
CROSSREFS
Row n=32 of A073133, A172236 and A352361 and column k=32 of A157103.
Sequence in context: A171306 A009976 A144319 * A158685 A265021 A159360
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 18 2013
STATUS
approved