

A041545


Denominators of continued fraction convergents to sqrt(290).


3



1, 34, 1157, 39372, 1339805, 45592742, 1551493033, 52796355864, 1796627592409, 61138134497770, 2080493200516589, 70797906952061796, 2409209329570617653, 81983915112353061998, 2789862323149574725585, 94937302902197893731888
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OFFSET

0,2


COMMENTS

Also called the 34metallonacci sequence; the g.f. 1/(1k*xx^2) gives the kmetallonacci sequence.
a(n) is the number of tilings of an nboard (a board with dimensions n X 1) using unit squares and dominoes (with dimensions 2 X 1) if there are 34 kinds of squares available. (End)


LINKS



FORMULA

a(n) = F(n, 34), the nth Fibonacci polynomial evaluated at x=34.  T. D. Noe, Jan 19 2006
a(n) = 34*a(n1) + a(n2) for n > 1; a(0)=1, a(1)=34.
G.f.: 1/(134*xx^2). (End)


MATHEMATICA

LinearRecurrence[{34, 1}, {1, 34}, 20] (* Harvey P. Dale, Oct 08 2021 *)


CROSSREFS



KEYWORD

nonn,frac,easy


AUTHOR



EXTENSIONS



STATUS

approved



