|
%I #22 Sep 08 2022 08:45:54
%S 0,1,83,6727,544895,44136511,3575057423,289579651327,23455951757615,
%T 1899932092367071,153894499481733263,12465454458020395327,
%U 1009701811099652023535,81785846699071813910431,6624653582624816926753103
%N a(n) = (81^n - 2^n)/79.
%C The a(n+1) appear in several triangle sums of Nicomachus's table A036561, i.e., Gi2(4*n), Gi2(4*n+1)/2, Gi2(4*n+2)/4, Gi2(4*n+3)/8 and Gi3(n). See A180662 for information about these giraffe and other chess sums.
%H Nathaniel Johnston, <a href="/A180846/b180846.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 (83,-162).
%F a(n) = (81^n - 2^n)/79.
%F G.f.: x/((81*x-1)*(2*x-1)).
%t Table[(81^n-2^n)/79,{n,0,15}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 13 2011 *)
%o (Magma) [(81^n-2^n)/79: n in [0..50]]; // _Vincenzo Librandi_, Apr 15 2011
%Y Cf. A016153, A016140, A180844, A180845, A180846, A180847, A016185.
%K easy,nonn
%O 0,3
%A _Johannes W. Meijer_, Sep 21 2010
|
