0,2

A floretion-generated sequence relating the squares of the numerators of continued fraction convergents to sqrt(2) to the squares of the denominators of continued fraction convergents to sqrt(2) (Pell numbers).

Index entries for sequences related to linear recurrences with constant coefficients

FAMP result: (-1)^(n+1) = A046729(n) - a(n) + 2*A090390(n+1) - 2*A079291(n+1) A046729 = 4*A084158 (Pell triangles) A090390(n) = A001333(n)^2 (Squares of "Numerators of continued fraction convergents to sqrt(2)") A079291(n) = A000129(n)^2 (Squares of Pell numbers) (see FAMP code for identity used) SuperSeeker results: a(n) + a(n+1) = A077444(n+1) (Numbers n such that (n^2+4)/2 is a square. Offset at 1.) a(n) + a(n+1) = A082639(n+2) - A082639(n+1) (Numbers n such that 2*n*(n+2) is a square.) a(n+2) - a(n) = A077444(n+3) - A077444(n+2) (Numbers n such that (n^2+4)/2 is a square. Offset at 1.) a(n) + 2*a(n+1) + a(n+2) = A077445(n+3) - A077445(n+2) (Numbers n such that (n^2-8)/2 is a square. Offset at 1.)

CoefficientList[ Series[(1 + 8x - x^2)/((x + 1)(x^2 - 6x + 1)), {x, 0, 19}], x] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 06 2005)

Floretion Algebra Multiplication Program, FAMP Code: 1dia[J]tesseq[ - .5'j + .5'k - .5j' + .5k' - 2'ii' + 'jj' - 'kk' + .5'ij' + .5'ik' + .5'ji' + 'jk' + .5'ki' + 'kj' + e ]. Identity used: dia[I]tes + dia[J]tes + dia[K]tes = jes + fam + 3tes.

Cf. A046729, A090390, A079291, A077444, A077445.

Equals 2*A001109(n+1) + (-1)^n.

Sequence in context: A137188 A055338 A055880 this_sequence A146469 A146381 A085461

Adjacent sequences: A105055 A105056 A105057 this_sequence A105059 A105060 A105061

nonn

Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Apr 04 2005

More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 06 2005.