5488420

Appears in sequences

• a(n) = 6*a(n-1) - a(n-2).at n=9A005319
• Numerators of continued fraction convergents to sqrt(18).at n=8A041026
• Numerators of continued fraction convergents to sqrt(162).at n=14A041298
• Numerators of continued fraction convergents to sqrt(242).at n=14A041452
• a(n) = 2*a(n-1) + a(n-2), with a(0) = 1, a(1) = 2, a(2) = 4.at n=18A052542
• Series ratios converge alternately to sqrt(2) and 1+sqrt(1/2).at n=36A082766
• Start with the sequence S(0)={1,1} and for k>0 define S(k) to be I(S(k-1)) where I denotes the operation of inserting, for i=1,2,3..., the term a(i)+a(i+1) between any two terms for which 4a(i+1)<=5a(i). The listed terms are the initial terms of the limit of this process as k goes to infinity.at n=35A082981
• 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=18A089499
• Expansion of g.f. (1+x)*(3+x)/(1+6*x^2+x^4).at n=17A100434
• Numerators of "Farey fraction" approximations to sqrt(2).at n=37A119016
• Numerators of principal and intermediate convergents to 2^(1/2).at n=34A143607
• A005319 and A002315 interleaved.at n=18A143608
• Numerators of fractions in a 'zero-transform' approximation of sqrt(2) by means of a(n) = (a(n-1) + c)/(a(n-1) + 1) with c=2 and a(1)=0.at n=18A163271
• Numerators of the best approximations for sqrt(2).at n=26A331115
• Lexicographically earliest sequence of distinct positive integers with no finite subset summing to a positive Pell number (A000129).at n=42A354005
• Square array, read by descending antidiagonals, where each row n comprises the integers w >= 1 such that A000037(n)*w^2+4 is a square.at n=36A378908