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%I #28 Sep 29 2024 16:02:16
%S 1,9,31,129,511,2049,8191,32769,131071,524289,2097151,8388609,
%T 33554431,134217729,536870911,2147483649,8589934591,34359738369,
%U 137438953471,549755813889,2199023255551,8796093022209,35184372088831,140737488355329,562949953421311
%N First differences of A140322.
%H Vincenzo Librandi, <a href="/A140323/b140323.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,4).
%F Mix A004171(2*n)-1, A004171(2*n+1)+1.
%F a(n+1)-4*a(n) = period 2: repeat [5, -5].
%F G.f.: x*(1 + 6*x)/(1 - 3*x - 4*x^2). - _Ilya Gutkovskiy_, May 11 2016
%F From _Klaus Purath_, Aug 03 2020: (Start)
%F a(n) = 8*A015521(n-1) + A102900(n-1).
%F a(n) = 30*4^(n-3) + a(n-2), n>2.
%F a(n+2) = 3*a(n+1) + 4*a(n). (End)
%t a[n_] := (2*4^n - (-1)^n); Array[a, 25, 0] (* _Robert G. Wilson v_, Aug 13 2011 *)
%Y Cf. A140322.
%K nonn,easy
%O 1,2
%A _Paul Curtz_, May 26 2008
%E Extended and offset changed from 0 to 1 by _Vincenzo Librandi_, Aug 09 2011