A105660 Expansion of g.f. (1-x)(x^2-5x+3)/(x^4-6x^3+13x^2-6x+1).

3, 10, 27, 49, 0, -485, -2643, -9602, -26163, -47525, 0, 470449, 2563707, 9313930, 25378083, 46099201, 0, -456335045, -2486793147, -9034502498, -24616714347, -44716177445, 0, 442644523201, 2412186788883, 8763458109130, 23878187538507

Offset

0,1

Comments

One of a set of interlinked sequences which appear to have the property that if a(m) = 0 for some m, then a(m+1), a(m+2), a(m+3), a(m+4), a(m+5) are strictly increasing or decreasing and a(m+6) = 0. Furthermore, for this particular sequence it would appear that a(m+3) is always even with a(m+1), a(m+2), a(m+4), a(m+5) odd. (a(n)) sequence is "ves" in the link to sequences in context. The identity ves = jes + les + tes holds.

Floretion Algebra Multiplication Program, FAMP Code: vesseq[ + .5'i - .5'j + .5i' + .5j' + .5k' - .5'ii' + .5'jj' - .5'ij' - .5'ik' + .5'ji' + .5'jk' + 1.5e]

Links

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (6,-13,6,-1).

Formula

For n > 11, a(n) = -970*a(n-6) - a(n-12). - Gerald McGarvey, Apr 21 2005

Mathematica

CoefficientList[ Series[(1 - x)(x^2 - 5x + 3)/(x^4 - 6x^3 + 13x^2 - 6x + 1), {x, 0, 26}], x] (* Robert G. Wilson v, Apr 18 2005 *)

Crossrefs

Sequence in context: A301308 A196232 A282282 * A056681 A192959 A100624

Adjacent sequences: A105657 A105658 A105659 * A105661 A105662 A105663

Keyword

easy,sign

Author

Creighton Dement, Apr 17 2005

Status

approved