1,2

B is of the form B(i)= 26*B(i-1) - B(i-2); B(0)=1;B(1)=25 (this sequence). A is of the form A(i)= 26*A(i-1) - A(i-2) ; A(0)=1 ; A(1)=27 . In general a Pell-like equation of the form 1 + X*A*A = (X+1)*B*B has the solution A(i) = (4*X+2)*A(i-1) - A(i-2) ; A(0)=1 ; A(1)=(4*X+3) and B(i) = (4*X+2)*B(i-1) - B(i-2) ; B(0)=1 ; B(1)=(4*X+1) . Examples in OEIS : X=1 gives A002315 for A(i) and A001653 for B(i), X=2 gives A054320 for A(i) and A072256 for B(i), X=3 gives A028230 for A(i) and A001570 for B(i), X=4 gives A049629 for A(i) and A007805 for B(i), X=5 gives A133283 for A(i) and {1,21,461,10121,...} for B(i), X=6 gives {1,27,701,...} for A(i) and this sequence for B(i).

Luigi Cimmino, Algebraic relations for recursive sequences. http://arxiv.org/abs/math/0510417v3

Jeroen Demeyer, Diophantine sets of polynomials over number fields. http://arxiv.org/abs/0807.1970v2

Franz Lemmermeyer, Conics - a Poor Man's Elliptic Curves. http://arxiv.org/abs/math/0311306v1

Index entries for sequences related to linear recurrences with constant coefficients

Cf. A002315, A001653, A054320, A072256, A001078, A028230, A001570, A049629, A007805, A133283, A140480,

Sequence in context: A009969 A042202 A152256 this_sequence A097194 A015697 A099365

Adjacent sequences: A153108 A153109 A153110 this_sequence A153112 A153113 A153114

easy,nonn

Ctibor O. Zizka (c.zizka(AT)email.cz), Dec 18 2008

More terms from Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 19 2009; corrected by N. J. A. Sloane, Sep 20 2009