A238055 - OEIS

%I #14 Aug 28 2023 14:29:32

%S 6,19,58,175,526,1579,4738,14215,42646,127939,383818,1151455,3454366,

%T 10363099,31089298,93267895,279803686,839411059,2518233178,7554699535,

%U 22664098606,67992295819,203976887458,611930662375,1835791987126,5507375961379,16522127884138

%N a(n) = (13*3^n-1)/2.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).

%F a(n) = 3*a(n-1) + 1, a(0)=6.

%F a(n) = 4*a(n-1) - 3*a(n-2), a(0)=6, a(1)=19.

%F a(n) = 2*A237930(n) - A003462(n).

%F a(n) = A052909(n+1) + A000244(n).

%F a(n) = A237930(n) + A000244(n+1).

%F a(n) = 13*A003462(n) + 6.

%F G.f.: (6-5*x)/((1-x)*(1-3*x)).

%F E.g.f.: exp(x)*(13*exp(2*x) - 1)/2. - _Stefano Spezia_, Aug 28 2023

%e Ternary....................Decimal

%e 20...............................6

%e 201.............................19

%e 2011............................58

%e 20111..........................175

%e 201111.........................526

%e 2011111.......................1579

%e 20111111......................4738

%e 201111111....................14215, etc.

%Y Cf. A000244, A003462, A052909, A060816, A237930.

%K nonn,easy

%O 0,1

%A _Philippe Deléham_, Feb 17 2014