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A173855 a(n) = A173039(n+4) - A173039(n+1).

%I A173855 #23 Sep 08 2022 08:45:50
%S A173855 8,4,24,40,12,56,72,20,88,104,28,120,136,36,152,168,44,184,200,52,216,
%T A173855 232,60,248,264,68,280,296,76,312,328,84,344,360,92,376,392,100,408,
%U A173855 424,108,440,456,116,472,488,124,504,520,132,536,552,140,568,584,148
%N A173855 a(n) = A173039(n+4) - A173039(n+1).
%C A173855 From Balmer odd terms. Note that ( (a(n+1)=8,) - (Balmer A061037 odd numbers = A173039(n+4) = 5, ) = 3, 1, 3, -5, -3, -21, ... = -A173039.
%H A173855 G. C. Greubel, <a href="/A173855/b173855.txt">Table of n, a(n) for n = 1..5000</a>
%H A173855 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,0,0,-1).
%F A173855 a(n) = 4*A173773(n).
%F A173855 a(n) = 2*a(n-3) - a(n-6). - _Colin Barker_, Oct 15 2014
%F A173855 G.f.: 4*x*(x+1)*(2*x^4 - x^3 + 7*x^2 - x + 2) / ((x-1)^2*(x^2 + x + 1)^2). - _Colin Barker_, Oct 15 2014
%e A173855 a(1) = 5 - (-3) = 8, a(2) = 3 - (-1) = 4, a(3) = 21 - (-3) = 24.
%p A173855 a:= LREtools[REtoproc](f(n) = 2*f(n-3)-f(n-6), f(n), zip((s,t)->f(s)=t, [$1..6],[8,4,24,40,12,56]),remember):
%p A173855 seq(a(n), n=1..100); # _Robert Israel_, Oct 15 2014
%t A173855 Rest[CoefficientList[Series[4*x*(x+1)*(2*x^4-x^3+7*x^2-x+2)/((x-1)^2*(x^2 +x+1)^2), {x, 0, 50}], x]] (* _G. C. Greubel_, Sep 20 2018 *)
%o A173855 (PARI) Vec(4*x*(x+1)*(2*x^4-x^3+7*x^2-x+2)/((x-1)^2*(x^2+x+1)^2) + O(x^100)) \\ _Colin Barker_, Oct 15 2014
%o A173855 (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(4*x*(x+1)*(2*x^4-x^3+7*x^2-x+2)/((x-1)^2*(x^2+x+1)^2))); // _G. C. Greubel_, Sep 20 2018
%Y A173855 Cf. A017113, A173039, A173773.
%K A173855 nonn,easy
%O A173855 1,1
%A A173855 _Paul Curtz_, Nov 26 2010
%E A173855 More terms from _Colin Barker_, Oct 15 2014