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%I #20 Mar 08 2024 12:14:19
%S 3,10,27,49,0,-485,-2643,-9602,-26163,-47525,0,470449,2563707,9313930,
%T 25378083,46099201,0,-456335045,-2486793147,-9034502498,-24616714347,
%U -44716177445,0,442644523201,2412186788883,8763458109130,23878187538507
%N Expansion of g.f. (1-x)(x^2-5x+3)/(x^4-6x^3+13x^2-6x+1).
%C 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.
%C 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]
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,6,-1).
%F For n > 11, a(n) = -970*a(n-6) - a(n-12). - _Gerald McGarvey_, Apr 21 2005
%t 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 *)
%K easy,sign
%O 0,1
%A _Creighton Dement_, Apr 17 2005
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