A189800 a(n) = 6*a(n-1) + 8*a(n-2), with a(0)=0, a(1)=1.

0, 1, 6, 44, 312, 2224, 15840, 112832, 803712, 5724928, 40779264, 290475008, 2069084160, 14738305024, 104982503424, 747801460736, 5326668791808, 37942424436736, 270267896954880, 1925146777223168, 13713023838978048, 97679317251653632, 695780094221746176

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,8).

Crossrefs

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

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

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

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

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

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

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

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

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

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

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

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

Programs

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

Mathematica

LinearRecurrence[{6, 8}, {0, 1}, 50]
CoefficientList[Series[-(x/(-1+6 x+8 x^2)),{x,0,50}],x] (* Harvey P. Dale, Jul 26 2011 *)

PARI

a(n)=([0,1; 8,6]^n*[0;1])[1,1] \\ Charles R Greathouse IV, Oct 03 2016

Formula

G.f.: x/(1 - 2*x*(3+4*x)). - Harvey P. Dale, Jul 26 2011