A103135 Expansion of (-3*x^3-18*x^2+14*x-1)/(3*x^4-5*x^2+4*x-1).

1, -10, -27, -55, -82, -83, -3, 238, 721, 1445, 2166, 2153, -55, -6650, -19827, -39599, -59426, -59659, -987, 175550, 528857, 1058701, 1587558, 1583377, -17711, -4811626, -14395275, -28772839, -43168114, -43243139, -317811, 128625934, 386588449, 773494709, 1160083158, 1158736889

Offset: 0

Author

Creighton Dement, Jan 24 2005

Keywords

• sign
• easy

Comments

A floretion-generated sequence which emerges as a transformation of A000004. a(6n+6)= A103134(n).

It appears that Fib(6n+1) = a(6n+4) - a(6n+5). - Creighton Dement, Jan 31 2005

Floretion Algebra Multiplication Program. FAMP code: 4lesforcycseq[ - .25'i + .5'j - .25i' - .5j' + .5k' - .25'ii' + .75'jj' - .25'kk' + .5'ji' + .25'jk' + .25'kj' + .75e ] Note: vesforcycseq = A000004, 4lesforseq gives A000045, vesseq gives A057681.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-5,0,3).

Crossrefs

Cf. A103134.

Programs

PARI

Vec((-3*x^3-18*x^2+14*x-1)/(3*x^4-5*x^2+4*x-1)+O(x^99)) \\ Charles R Greathouse IV, Feb 05 2013

Formula

a(n) = -9*A057083(n-1) - Fib(n-2). - Ralf Stephan, May 18 2007

a(n) = 4*a(n-1) - 5*a(n-2) + 3*a(n-4) for n>3. - Colin Barker, May 06 2019

Extensions

Definition not clear to me. A000004 is the zero sequence! N. J. A. Sloane.