1136689

Appears in sequences

• Pell numbers: a(0) = 0, a(1) = 1; for n > 1, a(n) = 2*a(n-1) + a(n-2).at n=17A000129
• Numbers k such that 2*k^2 - 1 is a square.at n=8A001653
• Markoff (or Markov) numbers: union of positive integers x, y, z satisfying x^2 + y^2 + z^2 = 3*x*y*z.at n=40A002559
• Interleave denominators (A000129) and numerators (A001333) of convergents to sqrt(2).at n=34A002965
• Primitive parts of Pell numbers.at n=16A008555
• Denominators of continued fraction convergents to sqrt(8).at n=16A041011
• Essentially a duplicate of A000129.at n=15A048624
• a(n) is the least natural number m such that the fractional part of m*(2^0.5) is less than 2^(-n).at n=19A058580
• a(n) is the least natural number m such that the fractional part of m*(2^0.5) is less than 2^(-n).at n=20A058580
• The next smallest pair of numbers is taken so that a(2n-1)/a(2n) converges to sqrt(2).at n=49A065375
• Number of 2 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.at n=14A069306
• Product representation of the Pell numbers A000129 and A002203.at n=33A072280
• Expansion of 1/(1 + 2*x - x^2).at n=16A077985
• a(0) = a(1) = 1; thereafter a(2*n+1) = 2*a(2*n) - a(2*n-1), a(2*n) = 4*a(2*n-1) - a(2*n-2).at n=17A079496
• Greedy frac multiples of sqrt(2): a(1)=1, Sum_{n>=0} frac(a(n)*x)=1 at x=sqrt(2).at n=23A079934
• a(0)=0; a(1)=1; a(2n) = 4*Sum_{k=0..n} a(2k-1); a(2n+1) = a(2n) + a(2n-1).at n=17A089499
• Interlaces "2*n^2 - 1 is a square" with NSW numbers.at n=16A104683
• Non-Fibonacci Markoff numbers.at n=25A111032
• Pythagorean triples of nearly isosceles triangle.at n=23A114336
• a(n) = 6*a(n-4) - a(n-8).at n=31A116558