A172241 - OEIS

%I #33 Oct 29 2023 13:57:19

%S 0,3,28,227,1820,14563,116508,932067,7456540,59652323,477218588,

%T 3817748707,30541989660,244335917283,1954687338268,15637498706147,

%U 125099989649180,1000799917193443,8006399337547548,64051194700380387

%N a(n) = (1/18)*(8^n - (-1)^n - 9).

%C It appears that a(n) = A153234(3*n-1). - _Bruno Berselli_, May 03 2011

%H Vincenzo Librandi, <a href="/A172241/b172241.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8, 1, -8).

%F G.f.: x^2*(3 + 4*x)/((1 - x)*(1 + x)*(1 - 8*x)). - Adapted to the offset by _Bruno Berselli_, May 03 2011

%F a(2*k) = 8*a(2*k-1) + 3 and a(2*k+1) = 8*a(2*k) + 4 for k>0, a(1)=0. - _Yosu Yurramendi_, Dec 30 2016

%p A172241:=n->(8^n-(-1)^n-9)/18: seq(A172241(n), n=1..30); # _Wesley Ivan Hurt_, May 02 2017

%t LinearRecurrence[{8,1,-8},{0,3,28},30] (* _Harvey P. Dale_, Oct 29 2023 *)

%o (PARI) a(n)=(8^n-(-1)^n-9)/18

%K nonn,easy

%O 1,2

%A _Ralf Stephan_, Nov 20 2010