login
a(n) = (8*5^n + 5*3^(n+1) - 5*2^n)/3.
1

%I #13 Oct 28 2022 06:23:08

%S 6,25,105,455,2045,9495,45205,219055,1074045,5305895,26335205,

%T 131090655,653692045,3263166295,16299929205,81451898255,407116166045,

%U 2035150690695,10174462707205,50868440641855,254330583216045

%N a(n) = (8*5^n + 5*3^(n+1) - 5*2^n)/3.

%H G. C. Greubel, <a href="/A147543/b147543.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 (10,-31,30).

%F From _R. J. Mathar_, Nov 09 2008: (Start)

%F a(n)= 10*a(n-1) -31*a(n-2) +30*a(n-3).

%F a(n) = (8*5^n + 5*3^(n+1) - 5*2^n)/3.

%F G.f.: (6 - 35*x + 41*x^2)/((1-2*x)*(1-3*x)*(1-5*x)). (End)

%F E.g.f.: (1/3)*( 8*exp(5*x) + 15*exp(3*x) - 5*exp(2*x) ). - _G. C. Greubel_, Oct 28 2022

%t LinearRecurrence[{10,-31,30}, {6,25,105}, 31] (* _G. C. Greubel_, Oct 28 2022 *)

%o (Magma) [(8*5^n +5*3^(n+1) -5*2^n)/3: n in [0..30]]; // _G. C. Greubel_, Oct 28 2022

%o (SageMath) [(8*5^n +5*3^(n+1) -5*2^n)/3 for n in range(31)] # _G. C. Greubel_, Oct 28 2022

%K nonn

%O 0,1

%A _Roger L. Bagula_, Nov 06 2008

%E Edited by _G. C. Greubel_, Oct 28 2022