A069005 Let M = 4 X 4 matrix with rows /1,1,1,1/1,1,1,0/1,1,0,0/1,0,0,0/ and A(n) = vector (x(n),y(n),z(n),t(n)) = M^n*A where A is the vector (1,1,1,1); then a(n)=z(n).

1, 7, 19, 56, 160, 462, 1329, 3828, 11021, 31735, 91376, 263108, 757588, 2181389, 6281058, 18085587, 52075371, 149945056, 431749580, 1243173370, 3579575053, 10306975580, 29677753369, 85453685055, 246054079584, 708484485384

Offset: 1

Author

Benoit Cloitre, Apr 02 2002

Keywords

• nonn
• easy

Comments

a(n) = A091024(n+1) for n > 1. - Georg Fischer, Oct 19 2018

Links

• Index entries for linear recurrences with constant coefficients, signature (2,3,-1,-1).

Crossrefs

Cf. A018919, A091024.

Programs

Mathematica

CoefficientList[Series[x (-x^4 - 2 x^3 + 2 x^2 + 5 x + 1)/((1 + x) (1 - 3 x + x^3)), {x, 0, 40}], x] (* Georg Fischer, May 24 2019 *)

Formula

G.f.: x*(-x^4-2*x^3+2*x^2+5*x+1)/((1+x)*(1-3*x+x^3)). [Corrected by Georg Fischer, May 24 2019]