%I #23 Jul 05 2023 16:24:42

%S 1,15,113,799,5601,39215,274513,1921599,13451201,94158415,659108913,

%T 4613762399,32296336801,226074357615,1582520503313,11077643523199,

%U 77543504662401,542804532636815,3799631728457713,26597422099203999,186181954694428001

%N a(n) = (7^(n+1) - 4) / 3.

%C Sum of n-th row of triangle of powers of 7: 1; 7 1 7; 49 7 1 7 49; 343 49 7 1 7 49 343; ...

%H Vincenzo Librandi, <a href="/A233326/b233326.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 (8,-7).

%F G.f.: (1+7*x)/((1-x)*(1-7*x)).

%F a(n) = 8*a(n-1) - 7*a(n-2) for n>1, a(0)=1, a(1)=15.

%F a(n) = 7*a(n-1) + 8 for n>0, a(0)=1.

%e a(0) = 1;

%e a(1) = 7 + 1 + 7 = 15;

%e a(2) = 49 + 7 + 1 + 7 + 49 = 113;

%e a(3) = 343 + 49 + 7 + 1 + 7 + 49 + 343 = 799; etc.

%t Table[(7^(n + 1) - 4)/3, {n, 0, 40}] (* _Vincenzo Librandi_, Feb 25 2014 *)

%t LinearRecurrence[{8,-7},{1,15},30] (* _Harvey P. Dale_, Jul 05 2023 *)

%o (Magma) [(7^(n+1)-4)/3: n in [0..30]]; // _Vincenzo Librandi_, Feb 25 2014

%K nonn,easy

%O 0,2

%A _Philippe Deléham_, Feb 23 2014