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%I #18 Sep 08 2022 08:45:35
%S 1,1,1,1,3,5,9,13,21,33,55,89,145,233,377,609,987,1597,2585,4181,6765,
%T 10945,17711,28657,46369,75025,121393,196417,317811,514229,832041,
%U 1346269,2178309,3524577,5702887,9227465,14930353,24157817,39088169
%N a(n) = A000045(n) + A131531(n+3).
%H Michael De Vlieger, <a href="/A141325/b141325.txt">Table of n, a(n) for n = 0..4786</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,1,1).
%F G.f.: (1-x^2+x^4)/((1+x)*(1-x+x^2)*(1-x-x^2)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009
%t LinearRecurrence[{1,1,-1,1,1}, {1,1,1,1,3}, 40] (* _Jean-François Alcover_, Aug 16 2017 *)
%t Table[Fibonacci@ n + Boole[Mod[n, 3] == 0] - 2 Boole[Mod[n, 6] == 3], {n, 0, 40}] (* _Michael De Vlieger_, Aug 16 2017 *)
%o (PARI) my(x='x+O('x^40)); Vec((1-x^2+x^4)/((1+x^3)*(1-x-x^2))) \\ _G. C. Greubel_, Jun 11 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x^2+x^4)/((1+x^3)*(1-x-x^2)) )); // _G. C. Greubel_, Jun 11 2019
%o (Sage) ((1-x^2+x^4)/((1+x^3)*(1-x-x^2))).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Jun 11 2019
%Y Cf. A014437, A140096, A140413.
%K nonn,easy
%O 0,5
%A _Paul Curtz_, Aug 03 2008
%E Definition corrected by _R. J. Mathar_, Sep 16 2009
%E More terms from _R. J. Mathar_, Sep 27 2009
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