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A074062 Reflected (see A074058) pentanacci numbers A074048.

%I A074062 #28 Aug 12 2023 21:13:52
%S A074062 5,-1,-1,-1,-1,9,-7,-1,-1,-1,19,-23,5,-1,-1,39,-65,33,-7,-1,79,-169,
%T A074062 131,-47,5,159,-417,431,-225,57,313,-993,1279,-881,339,569,-2299,3551,
%U A074062 -3041,1559,799,-5167,9401,-9633,6159,39,-11133,23969,-28667,21951,-6081,-22305
%N A074062 Reflected (see A074058) pentanacci numbers A074048.
%C A074062 a(n) is also the trace of A^(-n), where A is the matrix ( (1,1,0,0,0), (1,0,1,0,0), (1,0,0,1,0), (1,0,0,0,1), (1,0,0,0,0) ).
%C A074062 a(n) is also the sum of determinants of 4th-order principal minors of A^n.
%H A074062 G. C. Greubel, <a href="/A074062/b074062.txt">Table of n, a(n) for n = 0..1000</a>
%H A074062 Mario Catalani, <a href="http://arxiv.org/abs/math/0210201">Polymatrix and Generalized Polynacci Numbers</a>, arXiv:math/0210201 [math.CO], 2002.
%H A074062 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,-1,-1,1).
%F A074062 a(n) = -a(n-1) -a(n-2) -a(n-3) -a(n-4) +a(n-5), a(0)=5, a(1)=-1, a(2)=-1, a(3)=-1, a(4)=-1.
%F A074062 G.f.: (5 +4*x +3*x^2 +2*x^3 +x^4)/(1 +x +x^2 +x^3 +x^4 -x^5).
%t A074062 CoefficientList[Series[(5+4*x+3*x^2+2*x^3+x^4)/(1+x+x^2+x^3+x^4-x^5), {x, 0, 60}], x]
%o A074062 (PARI) Vec((5+4*x+3*x^2+2*x^3+x^4)/(1+x+x^2+x^3+x^4-x^5) + O(x^60)) \\ _Michel Marcus_, Sep 14 2020
%o A074062 (Magma) I:=[5,-1,-1,-1,-1]; [n le 5 select I[n] else (-1)*(Self(n-1) +Self(n-2) +Self(n-3) +Self(n-4)) + Self(n-5): n in [1..61]]; // _G. C. Greubel_, Jul 05 2021
%o A074062 (Sage)
%o A074062 def A074062_list(prec):
%o A074062     P.<x> = PowerSeriesRing(ZZ, prec)
%o A074062     return P( (5+4*x+3*x^2+2*x^3+x^4)/(1+x+x^2+x^3+x^4-x^5) ).list()
%o A074062 A074062_list(60) # _G. C. Greubel_, Jul 05 2021
%Y A074062 Cf. A061084, A074058, A074048.
%K A074062 easy,sign
%O A074062 0,1
%A A074062 Mario Catalani (mario.catalani(AT)unito.it), Aug 17 2002
%E A074062 More terms from _Michel Marcus_, Sep 14 2020