0,2

Also 7*x^2+1 is a square. n=7 in PARI script below. - Cino Hilliard (hillcino368(AT)gmail.com), Mar 08 2003

Except for the first term of [A001080] and of [A001081], if X=[A001081] (1,8,127,2024,32257,..,); Y=[A001080] (0,3,48,765,1192,..,) and A=[A010727] (7,7,7,..,) we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 8^2-7*3^2=1; 127^2-7*48^2=1; 2024^2-7*765^2=1; 32257^2-7*12192^2=1; [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 16 2009]

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

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (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.

H. Brocard, Notes e'le'mentaires sur le proble`me de Peel, Nouvelles Correspondance Math\'{e}matique, 4 (1878), 161-169.

V. Th\'{e}bault, Les R\'{e}cr\'{e}ations Math\'{e}matiques. Gauthier-Villars, Paris, 1952, p. 281.

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.: 3x/(1-16x+x^2).

a(n) = 15*(a(n-1)+a(n-2))-a(n-3). a(n) = 17*(a(n-1)-a(n-2))+a(n-3). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Sep 20 2006

a(n)=(1/14)*sqrt(7)*[8+3*sqrt(7)]^n-(1/14)*[8-3*sqrt(7)]^n*sqrt(7), with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Oct 02 2008]

A001080:=3*z/(1-16*z+z**2); [Conjectured by S. Plouffe in his 1992 dissertation.]

(PARI) nxsqp1(m, n) = { for(x=1, m, y = n*x*x+1; if(issquare(y), print1(x" ")) ) }

Equals 3 * A077412. Bisection of A084069. Cf. A048907.

Cf. A001081, A010727 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 16 2009]

Sequence in context: A081540 A024042 A007654 this_sequence A099852 A003029 A049524

Adjacent sequences: A001077 A001078 A001079 this_sequence A001081 A001082 A001083

nonn,easy

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

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 19 2000