A178676 - OEIS

%I #33 Dec 06 2023 13:54:10

%S 6,10,30,130,630,3130,15630,78130,390630,1953130,9765630,48828130,

%T 244140630,1220703130,6103515630,30517578130,152587890630,

%U 762939453130,3814697265630,19073486328130,95367431640630,476837158203130,2384185791015630,11920928955078130

%N a(n) = 5^n + 5.

%H Vincenzo Librandi, <a href="/A178676/b178676.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,-5).

%F a(n) = 5*(a(n-1) - 4) with a(0) = 6.

%F G.f.: (6-26*x)/((1-5*x)*(1-x)). - _R. J. Mathar_, Jan 05 2011

%F a(n) = 6*a(n-1) - 5*a(n-2) for n > 1. - _Vincenzo Librandi_, Sep 30 2013

%F E.g.f.: exp(5*x) + 5*exp(x). - _G. C. Greubel_, Jan 27 2019

%F a(n) = A000351(n)+5 = A034474(n)+4 = A242328(n)+3 = A242329(n)+1. - _Elmo R. Oliveira_, Dec 06 2023

%e G.f. = 6 + 10*x + 30*x^2 + 130*x^3 + 630*x^4 + 3130*x^5 + 15630*x^6 + ... - _Michael Somos_, Jan 28 2019

%t Table[5^n + 5, {n, 0, 40}] (* _Vincenzo Librandi_, Sep 30 2013 *)

%o (Magma) [5^n+5: n in [0..35]];

%o (PARI) a(n)=5^n+5 \\ _Charles R Greathouse IV_, Oct 07 2015

%o (Sage) [5^n+5 for n in range(40)] # _G. C. Greubel_, Jan 27 2019

%o (GAP) List([0..30], n -> 5^n +5); # _G. C. Greubel_, Jan 27 2019

%Y Cf. A000351, A034474, A178671, A242328, A242329.

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, Dec 25 2010