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).

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 A085461 A081860 A050403

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.