0,1

A156194=1,2,7,1,7,2,1,1,4,2,4,1,; (A156199=1,1,4,2,4,1,1,2,7,1,7,2,; correction in title: A000045 ,not Aoo1045). a(n)=A156194(4n)+A156194(4n+1)+A156194(4n+2)+A156194(4n+3); a(n)=A156199(4n+1)+A156199(4n+2)+A156199(4n+3)+A156199(4n+4). [From Paul Curtz (bpcrtz(AT)free.fr), Feb 06 2009]

If A=[A157040] 121*n.^2-2*n (n>0, 119, 480, 1083,.,. ,.,); Y=[A010850] 11 (11, 11, 11,.,); X=[A158130] 121*n-1 (n>0, 120, 241, 362, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 120^2-119*11^2=1; 241^2-480*11^2=1; 362^2-1083*11^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009]

If A=[A031689] 121*n.^2+2*n (n>0, 123, 488, 1095,.,. ,.,); Y=[A010850] 11 (11, 11, 11,.,); X=[A158131] 121*n+1 (n>0, 122, 243, 364, ,. .,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 122^2-123*11^2=1; 243^2-488*11^2=1; 364^2-1095*11^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009]

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

Cf. A157040, A158130 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009]

Cf. A031689, A158131 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 13 2009]

Sequence in context: A045538 A084066 A112122 this_sequence A113587 A083971 A052192

Adjacent sequences: A010847 A010848 A010849 this_sequence A010851 A010852 A010853

nonn

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