A002278 - OEIS

%I #46 Jun 16 2024 06:16:08

%S 0,4,44,444,4444,44444,444444,4444444,44444444,444444444,4444444444,

%T 44444444444,444444444444,4444444444444,44444444444444,

%U 444444444444444,4444444444444444,44444444444444444,444444444444444444,4444444444444444444,44444444444444444444,444444444444444444444

%N a(n) = 4*(10^n - 1)/9.

%H Ivan Panchenko, <a href="/A002278/b002278.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).

%F a(n) = A075415(n)/A002283(n). - _Reinhard Zumkeller_, May 31 2010

%F From _Vincenzo Librandi_, Jul 22 2010: (Start)

%F a(n) = a(n-1) + 4*10^(n-1) with a(0)=0;

%F a(n) = 11*a(n-1) - 10*a(n-2) with a(0)=0, a(1)=4. (End)

%F G.f.: 4*x/((1 - x)*(1 - 10*x)). - _Ilya Gutkovskiy_, Feb 24 2017

%F E.g.f.: 4*exp(x)*(exp(9*x) - 1)/9. - _Stefano Spezia_, Sep 13 2023

%F a(n) = A007091(A024049(n)). - _Michel Marcus_, Jun 16 2024

%t LinearRecurrence[{11, -10}, {0, 4}, 20] (* _Robert G. Wilson v_, Jul 06 2013 *)

%o (PARI) a(n)=4*(10^n-1)/9 \\ _Charles R Greathouse IV_, Sep 24 2015

%Y Cf. A002275, A002276, A002277, A002279, A002280, A002281, A002282, A002283, A075415, A178632.

%Y Cf. A007091, A024049.

%K easy,nonn

%O 0,2

%A _N. J. A. Sloane_