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A135055 Pentanacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) for n>4 and with a(0)=-2, a(1)=-1, a(2)=0, a(3)=1, a(4)=2.

%I A135055 #26 Feb 16 2025 08:33:07
%S A135055 -2,-1,0,1,2,0,2,5,10,19,36,72,142,279,548,1077,2118,4164,8186,16093,
%T A135055 31638,62199,122280,240396,472606,929119,1826600,3591001,7059722,
%U A135055 13879048,27285490,53641861,105457122,207323243,407586764,801294480,1575303470,3096965079,6088473036,11969622829
%N A135055 Pentanacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) for n>4 and with a(0)=-2, a(1)=-1, a(2)=0, a(3)=1, a(4)=2.
%H A135055 G. C. Greubel, <a href="/A135055/b135055.txt">Table of n, a(n) for n = 0..1000</a>
%H A135055 Piezas, Tito III and Weisstein, Eric W., <a href="https://mathworld.wolfram.com/PentanacciNumber.html">Pentanacci Number</a>
%H A135055 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,1).
%F A135055 From _R. J. Mathar_, Nov 18 2007: (Start)
%F A135055 G.f.: (1-2*x)*(x+1)*(2*x^2+x+2)/(-1+x+x^2+x^3+x^4+x^5).
%F A135055 a(n) = -2*A001591(n+4) + A001591(n+3) + 3*A001591(n+2) + 4*A001591(n+1) + 4*A001591(n). (End)
%t A135055 a[n_] := a[n] = a[n - 1] + a[n - 2] + a[n - 3] + a[n - 4] + a[n - 5]; a[0] = -2; a[1] = -1; a[2] = 0; a[3] = 1; a[4] = 2; Table[a[n], {n, 0, 50}] (* _Artur Jasinski_, Nov 15 2007 *)
%t A135055 LinearRecurrence[{1, 1, 1, 1, 1}, {-2, -1, 0, 1, 2}, 50] (* _G. C. Greubel_, Sep 21 2016 *)
%o A135055 (Magma) I:=[-2,-1,0,1,2]; [n le 5 select I[n] else Self(n-1)+Self(n-2)+Self(n-3)+Self(n-4)+Self(n-5): n in [1..40]]; // _Vincenzo Librandi_, Sep 22 2016
%Y A135055 Cf. A001591, A135056.
%K A135055 sign,easy
%O A135055 0,1
%A A135055 _Artur Jasinski_, Nov 15 2007