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%I #27 Mar 16 2024 11:04:14
%S 1,3,5,10,22,49,107,228,476,979,1993,4030,8114,16293,32663,65416,
%T 130936,261991,524117,1048386,2096942,4194073,8388355,16776940,
%U 33554132,67108539,134217377,268435078,536870506,1073741389,2147483183
%N Leading diagonal of triangle in A080521.
%H Vincenzo Librandi, <a href="/A080522/b080522.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,7,-2).
%F a(n) = 2^n-(n-1)*(n-2)/2-n+1 for n>1. - Lambert Herrgesell (zero815(AT)googlemail.com), Mar 14 2006
%F a(n) = A014844(n), n>1. - _R. J. Mathar_, Sep 19 2008
%F From _Colin Barker_, Dec 18 2012: (Start)
%F a(n) = 5*a(n-1)-9*a(n-2)+7*a(n-3)-2*a(n-4) for n>5.
%F G.f.: -x*(2*x^4-5*x^3+x^2+2*x-1) / ((x-1)^3*(2*x-1)). (End)
%t Join[{1}, Array[2^# - #*(# - 1)/2 &, 50, 2]] (* _Paolo Xausa_, Mar 16 2024 *)
%o (Magma) [1] cat[2^n-(n-1)*(n-2)/2-n+1: n in [2..40]]; // _Vincenzo Librandi_, Apr 18 2012
%Y Cf. A080521.
%K nonn,easy
%O 1,2
%A _Amarnath Murthy_, Mar 21 2003
%E More terms from Lambert Herrgesell (zero815(AT)googlemail.com), Mar 14 2006
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