161564

Appears in sequences

• a(n) = 6*a(n-1) - a(n-2).at n=7A005319
• Sum of odd divisors of n < sqrt(n) = sum of even divisors of n < sqrt(n).at n=16A033832
• Numerators of continued fraction convergents to sqrt(18).at n=6A041026
• a(n) = 2*a(n-1) + a(n-2), with a(0) = 1, a(1) = 2, a(2) = 4.at n=14A052542
• The next smallest pair of numbers is taken so that a(2n-1)/a(2n) converges to sqrt(2).at n=40A065375
• Series ratios converge alternately to sqrt(2) and 1+sqrt(1/2).at n=28A082766
• 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=27A082981
• 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=14A089499
• a(n) = (a(n-1) mod 2)*a(n-1) + a(n-2) with a(0)=0, a(1)=1.at n=42A097564
• Expansion of g.f. (1+x)*(3+x)/(1+6*x^2+x^4).at n=13A100434
• Numerators of "Farey fraction" approximations to sqrt(2).at n=29A119016
• Numerators of principal and intermediate convergents to 2^(1/2).at n=26A143607
• A005319 and A002315 interleaved.at n=14A143608
• 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=14A163271
• a(n) = Pell(n)*A001227(n) for n >= 1, where A001227(n) is the number of odd divisors of n.at n=13A209445
• Two column recursive array A(n,k), relating expressions based on half-squares (A007590) to each other and several other sequences, read by rows.at n=43A227972
• List of triples (r,s,t): the matrix M = [[1,4,4][1,3,2][1,2,1]] is raised to successive powers, then (r,s,t) are the square roots of M[3,1], M[1,1], M[1,3] respectively.at n=44A249576
• Numerators of the best approximations for sqrt(2).at n=20A331115
• Numbers m such that there exists at least one integer k < m where m^2 + 2 and k^2 + 2 have the same prime factors.at n=42A348889
• Lexicographically earliest sequence of distinct positive integers with no finite subset summing to a positive Pell number (A000129).at n=32A354005