1607521

Appears in sequences

• Pell-Lucas numbers: numerators of continued fraction convergents to sqrt(2).at n=17A001333
• NSW numbers: a(n) = 6*a(n-1) - a(n-2); also a(n)^2 - 2*b(n)^2 = -1 with b(n) = A001653(n+1).at n=8A002315
• Interleave denominators (A000129) and numerators (A001333) of convergents to sqrt(2).at n=35A002965
• Primitive parts of Pell numbers.at n=33A008555
• The next smallest pair of numbers is taken so that a(2n-1)/a(2n) converges to sqrt(2).at n=48A065375
• Number of 16 X n binary arrays with a path of adjacent 1's from top row to bottom row.at n=1A069374
• Product representation of the Pell numbers A000129 and A002203.at n=16A072280
• Expansion of (1+x)/(1-2*x-x^2).at n=16A078057
• Series ratios converge alternately to sqrt(2) and 1+sqrt(1/2).at n=33A082766
• a(1) = 1, a(2) = 2; a(2*k) = 2*a(2*k-1) - a(2*k-2), a(2*k+1) = 4*a(2*k) - a(2*k-1).at n=16A084068
• Expansion of e.g.f.: cosh(sqrt(2)*x)*(1+exp(x)).at n=17A088014
• Composite NSW numbers.at n=4A094666
• Expansion of (1+2*x-2*x^3-3*x^2)/((x-1)*(x+1)*(x^2+2*x-1)).at n=16A100828
• Interlaces "2*n^2 - 1 is a square" with NSW numbers.at n=17A104683
• a(2n) = A002315(n), a(2n+1) = A082639(n+1).at n=16A113224
• Logarithmic derivative of the g.f. of A113281.at n=16A113282
• Numerators of "Farey fraction" approximations to sqrt(2).at n=34A119016
• Fixed-k dispersion for Q = 8: Square array D(g,h) (g, h >= 1), read by ascending antidiagonals.at n=44A120861
• Shifted Pell recurrence: a(n) = 2*a(n-2) + a(n-4).at n=31A135246
• Numerators of principal and intermediate convergents to 2^(1/2).at n=31A143607