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.

-2, -1, 0, 1, 2, 0, 2, 5, 10, 19, 36, 72, 142, 279, 548, 1077, 2118, 4164, 8186, 16093, 31638, 62199, 122280, 240396, 472606, 929119, 1826600, 3591001, 7059722, 13879048, 27285490, 53641861, 105457122, 207323243, 407586764, 801294480, 1575303470, 3096965079, 6088473036, 11969622829

Offset: 0

Author

Artur Jasinski, Nov 15 2007

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Piezas, Tito III and Weisstein, Eric W., Pentanacci Number
• Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1).

Crossrefs

Cf. A001591, A135056.

Programs

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

Mathematica

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 *)
LinearRecurrence[{1, 1, 1, 1, 1}, {-2, -1, 0, 1, 2}, 50] (* G. C. Greubel, Sep 21 2016 *)

Formula

From R. J. Mathar, Nov 18 2007: (Start)

G.f.: (1-2*x)*(x+1)*(2*x^2+x+2)/(-1+x+x^2+x^3+x^4+x^5).

a(n) = -2*A001591(n+4) + A001591(n+3) + 3*A001591(n+2) + 4*A001591(n+1) + 4*A001591(n). (End)