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%I #6 Oct 23 2016 10:45:44
%S 1,-4,0,1,-5,4,1,-6,9,-3,-7,15,-12,-4,22,-27,8,26,-49,35,18,-75,84,
%T -17,-93,159,-101,-76,252,-260,25,328,-512,285,303,-840,797,18,-1143,
%U 1637,-779,-1161,2780,-2416,-382,3941,-5196,2034,4323,-9137,7230,2289,-13460,16367,-4941,-15749,29827,-21308,-10808
%N a(n+4) = a(n+1) - a(n), a(0) = 1, a(1) = -4, a(2) = 0, a(3) = 1.
%C One of several sequences, apparently all of the form a(n+4) = a(n+1) - a(n), which appear to "spiral outwards" when plotted against each other (see A110061-64). In reference to the FAMP program code, A017817 is also in this same batch of sequences and satisfies the same recurrence relation.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,-1).
%F Expansion of (4*x-1)/(1-x^3+x^4)
%p seriestolist(series(-(-1+4*x)/(1-x^3+x^4), x=0,60)); -or- Floretion Algebra Multiplication Program, FAMP Code: 4kbaseseq[A*B] with A = + .5'i + .5'j + .5'k + .5e and B = - .5'i - .25'j + .25'k - .5i' - .25j' + .25k' - .5'ii' - .25'ij' - .25'ik' - .25'ji' - .25'ki' - .5e
%t LinearRecurrence[{0,0,1,-1},{1,-4,0,1},60] (* _Harvey P. Dale_, Oct 23 2016 *)
%Y Cf. A110061, A110062, A110063, A017817.
%K easy,sign
%O 0,2
%A _Creighton Dement_, Jul 10 2005
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