A078058 - OEIS

%I #20 May 03 2023 15:16:52

%S 1,-3,7,-18,46,-117,298,-759,1933,-4923,12538,-31932,81325,-207120,

%T 527497,-1343439,3421495,-8713926,22192786,-56520993,143948698,

%U -366611175,933692041,-2377943955,6056191126,-15424018248,39282171577,-100044552528,254795294881,-648917313867

%N Expansion of (1-x)/(1+2*x-x^2+x^3).

%C a(n) is the upper left entry of the n-th power of the 3 X 3 matrix M = [-3, -3, 1; 1, 1, 0; 1, 0, 0]; a(n) = M^n [1, 1]. - _Philippe Deléham_, Apr 19 2023

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-2,1,-1).

%F a(n) = -2*a(n-1) + a(n-2) - a(n-3) for n > 2; a(0) = 1, a(1) = -3, a(2) = 7. - _Harvey P. Dale_, Oct 22 2011

%F a(n) = Sum_{k = 0..n} A188316(n, k)*(-3)^k. - _Philippe Deléham_, Apr 19 2023

%t CoefficientList[Series[(1-x)/(1+2x-x^2+x^3),{x,0,30}],x] (* or *) LinearRecurrence[{-2,1,-1},{1,-3,7},31] (* _Harvey P. Dale_, Oct 22 2011 *)

%o (PARI) Vec((1-x)/(1+2*x-x^2+x^3)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 27 2012

%K sign,easy

%O 0,2

%A _N. J. A. Sloane_, Nov 17 2002