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%I #19 Sep 08 2022 08:45:09
%S 1,3,8,16,31,57,106,198,377,727,1420,2796,5539,11013,21950,43810,
%T 87517,174915,349696,699240,1398311,2796433,5592658,11185086,22369921,
%U 44739567,89478836,178957348,357914347,715828317,1431656230,2863312026
%N Partial sums of A081660.
%H Vincenzo Librandi, <a href="/A081661/b081661.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-2,5,-2).
%F a(n) = 2^(n+2)/3+(n^2+n-1)/2+(-1)^n/6.
%F G.f.: (1-x-2*x^3)/((1+x)*(1-2*x)*(1-x)^3). - _Bruno Berselli_, Aug 11 2013
%p A081661:=n->2^(n+2)/3 + (n^2+n-1)/2 + (-1)^n/6; seq(A081661(n), n=0..30); # _Wesley Ivan Hurt_, May 07 2014
%t Table[2^(n + 2) / 3 + (n^2 + n - 1) / 2 + (-1)^n / 6, {n, 0, 40}] (* _Vincenzo Librandi_, Aug 10 2013 *)
%t LinearRecurrence[{4,-4,-2,5,-2},{1,3,8,16,31},40] (* _Harvey P. Dale_, Jan 11 2016 *)
%o (Magma) [2^(n+2)/3+(n^2+n-1)/2+(-1)^n/6: n in [0..40]]; // _Vincenzo Librandi_, Aug 10 2013
%Y Cf. A001045, A081660.
%K nonn,easy
%O 0,2
%A _Paul Barry_, Mar 26 2003
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