941664

Appears in sequences

• a(n) = 6*a(n-1) - a(n-2).at n=8A005319
• a(n) = 2*a(n-1) + a(n-2), with a(0) = 1, a(1) = 2, a(2) = 4.at n=16A052542
• The next smallest pair of numbers is taken so that a(2n-1)/a(2n) converges to sqrt(2).at n=46A065375
• Series ratios converge alternately to sqrt(2) and 1+sqrt(1/2).at n=32A082766
• 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=31A082981
• 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=16A089499
• Numerators of "Farey fraction" approximations to sqrt(2).at n=33A119016
• Numerators of principal and intermediate convergents to 2^(1/2).at n=30A143607
• A005319 and A002315 interleaved.at n=16A143608
• 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=16A163271
• Number of (n+4)X(n+4) binary arrays with every 5X5 subblock commuting with each horizontal and vertical neighbor 5X5 subblock.at n=13A186600
• a(n) = Pell(n)*A113973(n) for n>=1, with a(0)=1, where A113973 lists the coefficients in phi(x^3)^3/phi(x) and phi() is a Ramanujan theta function.at n=16A209449
• 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=49A227972
• 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=50A249576
• Numerators of the best approximations for sqrt(2).at n=23A331115
• Lexicographically earliest sequence of distinct positive integers with no finite subset summing to a positive Pell number (A000129).at n=37A354005
• 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=28A378908