login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3) (n >= 3) with a(0) = a(1) = 1, a(2) = 2.
1

%I #20 Jul 07 2024 11:58:22

%S 1,1,2,9,46,221,1002,4369,18566,77541,320002,1309529,5326686,21572461,

%T 87087002,350739489,1410132406,5662052981,22712782002,91044838249,

%U 364760483726,1460785327101,5848371485002,23409176469809,93683777468646

%N a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3) (n >= 3) with a(0) = a(1) = 1, a(2) = 2.

%C The above sequence also satisfies a(n) - 7*a(n-1) + 12*a(n-2) = 7 (n >= 2) with a(0)=a(1)=1.

%H Harvey P. Dale, <a href="/A162725/b162725.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-19,12).

%F a(n) = 4^n/3 - 3^n/2 + 7/6. - _Emeric Deutsch_, Jul 19 2009

%F G.f.: -(1-7*x+13*x^2)/((x-1)*(3*x-1)*(4*x-1)). - _R. J. Mathar_, Jul 31 2009

%p seq(7/6-(1/2)*3^n+(1/3)*4^n, n = 0 .. 25); # _Emeric Deutsch_, Jul 19 2009

%t LinearRecurrence[{8,-19,12},{1,1,2},30] (* _Harvey P. Dale_, Jul 07 2024 *)

%K nonn,easy

%O 0,3

%A Tian-Xiao He (the(AT)iwu.edu), Jul 11 2009

%E More terms from _Vincenzo Librandi_, Jul 13 2009

%E Extended by _Emeric Deutsch_, Jul 19 2009