%I #50 Apr 11 2024 15:19:45

%S 0,1,6,44,312,2224,15840,112832,803712,5724928,40779264,290475008,

%T 2069084160,14738305024,104982503424,747801460736,5326668791808,

%U 37942424436736,270267896954880,1925146777223168,13713023838978048,97679317251653632,695780094221746176

%N a(n) = 6*a(n-1) + 8*a(n-2), with a(0)=0, a(1)=1.

%H Vincenzo Librandi, <a href="/A189800/b189800.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,8).

%F G.f.: x/(1 - 2*x*(3+4*x)). - _Harvey P. Dale_, Jul 26 2011

%t LinearRecurrence[{6, 8}, {0, 1}, 50]

%t CoefficientList[Series[-(x/(-1+6 x+8 x^2)),{x,0,50}],x] (* _Harvey P. Dale_, Jul 26 2011 *)

%o (Magma) I:=[0,1]; [n le 2 select I[n] else 6*Self(n-1)+8*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Nov 14 2011

%o (PARI) a(n)=([0,1; 8,6]^n*[0;1])[1,1] \\ _Charles R Greathouse IV_, Oct 03 2016

%Y Sequences of the form a(n) = c*a(n-1) + d*a(n-2), with a(0)=0, a(1)=1:

%Y c/d...1.......2.......3.......4.......5.......6.......7.......8.......9......10

%Y 1..A000045,A001045,A006130,A006131,A015440,A015441,A015442,A015443,A015445,A015446

%Y 2..A000129,A002605,A015518,A063727,A002532,A083099,A015519,A003683,A002534,A083102

%Y 3..A006190,A007482,A030195,A015521,A015523,A083858,A015524,A015525,A099012,A015528

%Y 4..A001076,A090017,A015530,A057087,A015531,A085939,A015532,A180222,A015533,A180226

%Y 5..A052918,A015535,A015536,A015537,A057088,A015540,A015541,A015544,A015545,A180250

%Y 6..A005668,A135030,A090018,A135032,A015551,A057089,A015552,A189800,A189801,A190005

%Y 7..A054413,A015555,A015559,A015561,A015562,A015564,A057090,A015565,A015566,A015568

%Y 8..A041025,A190331,A015574,A190510,A015575,A190560,A015576,A057091,A015577,A190953

%Y 9..A099371,A015579,A181353,A015580,A015581,A153191,A015583,A015584,A057092,A015585

%Y 10.A041041,A191014,A015588,A190954,A190955,A190956,A015589,A190957,A015591,A057093

%K nonn,easy

%O 0,3

%A _Vladimir Joseph Stephan Orlovsky_, May 24 2011