A129997 - OEIS

%I #15 Sep 08 2022 08:45:30

%S 0,1,4,14,52,208,884,3952,18460,89648,450892,2341456,12522068,

%T 68819920,387978292,2240112368,13228210684,79794191152,491143503500,

%U 3081692690128,19693923313012,128082776294096,847127801497588

%N a(n) = 4*a(n-1) + (n-6)*a(n-2).

%F a(n) = 4*a(n-1) + (n-6)*a(n-2). - _Vaclav Kotesovec_, Oct 20 2012

%F a(n) ~ 26*sqrt(2)*exp(4*sqrt(n)-n/2-4)*n^(n/2-5/2)*(1-19/(3*sqrt(n))+1/(6*n)) . - _Vaclav Kotesovec_, Oct 20 2012

%t M[n_] := {{0, 1}, {-4 + n, 4}} v[0] = {0, 1}; v[n_] := v[n] = M[n].v[m - 1] a = Table[v[m][[1]], {m, 0, 30}]

%t RecurrenceTable[{a[n] == 4*a[n-1] + (n-6)*a[n-2],a[1]==0,a[2]==1},a,{n,20}] (* _Vaclav Kotesovec_, Oct 20 2012 *)

%o (Magma) [n le 2 select n-1 else 4*Self(n-1)+(n-6)*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, May 24 2013

%K nonn

%O 1,3

%A _Roger L. Bagula_, Jun 15 2007

%E New name from _Vaclav Kotesovec_, Oct 20 2012