A102485 - OEIS

%I #35 Jul 16 2024 13:29:38

%S 1,7,29,103,341,1087,3389,10423,31781,96367,291149,877543,2640821,

%T 7938847,23849309,71613463,214971461,645176527,1936053869,5809210183,

%U 17429727701,52293377407,156888520829,470682339703,1412080573541,4236308829487,12709060706189

%N a(n) = 5*3^n - 4*2^n.

%D B. M. E. Moret and H. D. Shapiro, Algorithms from P to NP, Benjamin/Cummings, Vol. 1, 1991; p. 63.

%H Vincenzo Librandi, <a href="/A102485/b102485.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 (5,-6).

%F a(n) = 5*a(n - 1) - 6*a(n - 2).

%F G.f.: (1+2*x)/((1-2*x)*(1-3*x)). - _Colin Barker_, Jan 14 2012

%F a(n) = A217764(n,8). - _Ross La Haye_, Mar 27 2013

%F a(n) = A001047(n+1)+2*A001047(n). - _R. J. Mathar_, May 14 2024

%p a := proc(n) option remember; if n = 0 then RETURN(1) end if; if n = 1 then RETURN(7) end if; 5*a(n - 1) - 6*a(n - 2); end proc;

%t LinearRecurrence[{5,-6},{1,7},30] (* _Vincenzo Librandi_, Jan 15 2012 *)

%t Table[5*3^n-4*2^n,{n,0,30}] (* _Harvey P. Dale_, Jul 16 2024 *)

%o (Magma) I:=[1, 7]; [n le 2 select I[n] else 5*Self(n-1)-6*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Jan 15 2012

%o (PARI) a(n)=5*3^n-4<<n \\ _Charles R Greathouse IV_, Jan 15 2012

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Feb 25 2005

%E New definition from _Ralf Stephan_, May 17 2007