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A040137 Continued fraction for sqrt(150). 0
12, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4, 24, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..73.

Index entries for continued fractions for constants

Index entries for linear recurrences with constant coefficients, signature (0,1).

FORMULA

a(n) = 14+10*(-1)^n-12*[C(2*n,n) mod 2], with n>=0. [Paolo P. Lava, Jun 10 2009]

MAPLE

Digits := 100: convert(evalf(sqrt(N)), confrac, 90, 'cvgts'):

MATHEMATICA

ContinuedFraction[Sqrt[150], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 13 2011*)

PROG

(Python)

from sympy import sqrt

from sympy.ntheory.continued_fraction import continued_fraction_iterator

def aupton(nn):

    gen = continued_fraction_iterator(sqrt(150))

    return [next(gen) for i in range(nn+1)]

print(aupton(73)) # Michael S. Branicky, Dec 04 2021

(Python) # second version based on recurrence

def a(n): return 12 if n == 0 else [4, 24][(n-1)%2]

print([a(n) for n in range(74)]) # Michael S. Branicky, Dec 04 2021

CROSSREFS

Sequence in context: A339467 A199693 A166206 * A092237 A081987 A327972

Adjacent sequences:  A040134 A040135 A040136 * A040138 A040139 A040140

KEYWORD

nonn,cofr,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified January 28 14:26 EST 2022. Contains 350656 sequences. (Running on oeis4.)