A123102 - OEIS

%I #15 Aug 07 2022 07:39:14

%S 1,0,1,4,5,12,29,56,121,264,553,1180,2525,5364,11429,24368,51889,

%T 110544,235537,501748,1068917,2277276,4851437,10335464,22018729,

%U 46908504,99933625,212898316,453557453,966256644,2058509045,4385438048

%N a(0)=1, a(1)=0, a(2)=1, a(n) = a(n-1) + a(n-2) + 3*a(n-3).

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,3).

%F a(n) + a(n+1) = A099213(n+1).

%F G.f.: (1-x)/(1-x-x^2-3*x^3).

%F If p[1]=0, p[2]=1, p[i]=4, (i>2), and if A is Hessenberg matrix of order n defined by: A[i,j]=p[j-i+1], (i<=j), A[i,j]=-1, (i=j+1), and A[i,j]=0 otherwise, then, for n>=1, a(n)=det A. - _Milan Janjic_, May 02 2010

%t LinearRecurrence[{1,1,3},{1,0,1},40] (* _Harvey P. Dale_, May 04 2018 *)

%o (PARI) Vec((1-x)/(1-x-x^2-3*x^3) + O(x^40)) \\ _Michel Marcus_, Aug 07 2022

%Y Cf. A099213.

%K nonn,easy

%O 0,4

%A _Philippe Deléham_, Sep 27 2006

%E Corrected by _T. D. Noe_, Nov 07 2006