0,2

A floretion-generated sequence resulting from a particular transform of the periodic sequence (-1,1).

Also indices of the centered triangular numbers which are triangular numbers - R. Choulet (richardchoulet(AT)yahoo.fr), Oct 09 2007

2a(n) - A001834(n) = (-1)^(n+1); a(n) = 4a(n-1) - a(n) - 1; G.f. x(2x-1)/((x-1)(x^2-4x+1)). Superseeker results: a(n+2) - 2a(n+1) + a(n) = A001834(n+1) (from this and the first relation involving A001834 it follows that 4a(n+1) - a(n+2) - a(n) = (-1)^n as well as the recurrence relation given for A001834 ); a(n+1) - a(n) = A001075(n+1) (Chebyshev's T(n, x) polynomials evaluated at x=2); a(n+2) - a(n) = A082841(n+1)

a[j+3]-3*a[j+2]-3*a[j+1]+a[j] = -2 for all j.

a(n+1)=2*a(n)-0.5+0.5*(12*a(n)^2-12*a(n)+9)^0.5 - R. Choulet (richardchoulet(AT)yahoo.fr), Oct 09 2007

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=4*a[n-1]-a[n-2]-1 od: seq(a[n], n=1..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 08 2008

Floretion Algebra Multiplication Program, FAMP Code: .5em[J* ]forseq[ .25( 'i + 'j + 'k + i' + j' + k' + 'ii' + 'jj' + 'kk' + 'ij' + 'ik' + 'ji' + 'jk' + 'ki' + 'kj' + e ) ], em[J]forseq = A001834, vesforseq = (1, -1, 1, -1). ForType 1A. Identity used: em[J]forseq + em[J* ]forseq = vesforseq.

Cf. A001834, A001075, A082841.

Sequence in context: A047122 A047107 A055989 this_sequence A119374 A126188 A081909

Adjacent sequences: A102868 A102869 A102870 this_sequence A102872 A102873 A102874

nonn

Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Mar 01 2005

More terms from R. Choulet (richardchoulet(AT)yahoo.fr), Oct 09 2007