%I #27 Feb 10 2024 03:44:18
%S 1,17,145,1169,9361,74897,599185,4793489,38347921,306783377,
%T 2454267025,19634136209,157073089681,1256584717457,10052677739665,
%U 80421421917329,643371375338641,5146971002709137,41175768021673105,329406144173384849,2635249153387078801
%N a(n) = (2*8^(n+1) - 9) / 7.
%C Sum of n-th row of triangle of powers of 8: 1; 8 1 8; 64 8 1 8 64 ; 512 64 8 1 8 64 512; ...
%H Vincenzo Librandi, <a href="/A233328/b233328.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 (9,-8).
%F G.f.: (1+8*x)/((1-x)*(1-8*x)).
%F a(n) = 9*a(n-1) - 8*a(n-2) for n>1, a(0)=1, a(1)=17.
%F a(n) = 8*a(n-1) + 9 for n>0, a(0)=1.
%F a(n) = A226308(3n+1).
%e a(0) = 1;
%e a(1) = 8 + 1 + 8 = 17;
%e a(2) = 64 + 8 + 1 + 8 + 64 = 145;
%e a(3) = 512 + 64 + 8 + 1 + 8 + 64 + 512 = 1169; etc.
%t Table[(2 8^(n + 1) - 9)/7, {n, 0, 30}] (* _Vincenzo Librandi_, Feb 25 2014 *)
%t LinearRecurrence[{9,-8},{1,17},30] (* _Harvey P. Dale_, Apr 29 2019 *)
%o (Magma) [(2*8^(n+1)-9)/7: n in [0..30]]; // _Vincenzo Librandi_, Feb 25 2014
%Y Cf. A226308
%K nonn,easy
%O 0,2
%A _Philippe Deléham_, Feb 23 2014