0,2

Solutions y of the equation 2x^2-y^2=2; the corresponding x values are given by A001541. - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Feb 25 2008

The lower intermediate convergents to 2^(1/2) beginning with 4/3, 24/17, 140/99, 816/577, form a strictly increasing sequence; essentially, numerators=A005319 and denominators=A001541. - Clark Kimberling (ck6(AT)evansville.edu), Aug 26 2008

Numbers n such that (ceiling(sqrt(n*n/2)))^2 = 1 + n*n/2 [From Ctibor O. Zizka (c.zizka(AT)email.cz), Nov 09 2009]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 160, middle display.

Index entries for sequences related to linear recurrences with constant coefficients

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

Tanya Khovanova, Recursive Sequences

G.f. for signed version beginning with 1: (1+2*x+x^2)/(1+6*x+x^2).

For any term n of the sequence, 2*n^2 + 4 is a perfect square. Lim a(n)/a(n-1) = 3 + 2*Sqrt(2) - Gregory V. Richardson (omomom(AT)hotmail.com), Oct 06 2002

a(n) = [(3+2*Sqrt(2))^n - (3-2*Sqrt(2))^n] / Sqrt(2) - Gregory V. Richardson (omomom(AT)hotmail.com), Oct 06 2002

(-1)^(n+1) = A090390(n+1) + A001542(n+1) + A046729(n) - a(n) (conjectured). Generated by the floretion - .5'i + .5'j - .5i' + .5j' + 'ii' - 'jj' - 2'kk' + 'ij' + .5'ik' + 'ji' + .5'jk' + .5'ki' + .5'kj' + e - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Nov 17 2004

For n>0, a(n)=A000129(n+1)^2-A000129(n-1)^2; e.g. 816=29^2-5^2; a(n)=A046090(n-1)+A001652(n); e.g. 816=120+696; a(n)=A001653(n)-A001653(n-1); e.g. 816=985-169 - Charlie Marion (charliemath(AT)optonline.net) Jul 22 2005

a(n)=4*A001109(n). [M. Hasler, Mar 2009] [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 03 2009]

A005319:=4*z/(1-6*z+z**2); [Conjectured by S. Plouffe in his 1992 dissertation.]

Sequence in context: A071079 A153337 A122690 this_sequence A155119 A114169 A121102

Adjacent sequences: A005316 A005317 A005318 this_sequence A005320 A005321 A005322

nonn,new

N. J. A. Sloane (njas(AT)research.att.com).