A081661 Partial sums of A081660.
1, 3, 8, 16, 31, 57, 106, 198, 377, 727, 1420, 2796, 5539, 11013, 21950, 43810, 87517, 174915, 349696, 699240, 1398311, 2796433, 5592658, 11185086, 22369921, 44739567, 89478836, 178957348, 357914347, 715828317, 1431656230, 2863312026
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-4,-2,5,-2).
Programs
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Magma
[2^(n+2)/3+(n^2+n-1)/2+(-1)^n/6: n in [0..40]]; // Vincenzo Librandi, Aug 10 2013
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Maple
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
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Mathematica
Table[2^(n + 2) / 3 + (n^2 + n - 1) / 2 + (-1)^n / 6, {n, 0, 40}] (* Vincenzo Librandi, Aug 10 2013 *) LinearRecurrence[{4,-4,-2,5,-2},{1,3,8,16,31},40] (* Harvey P. Dale, Jan 11 2016 *)
Formula
a(n) = 2^(n+2)/3+(n^2+n-1)/2+(-1)^n/6.
G.f.: (1-x-2*x^3)/((1+x)*(1-2*x)*(1-x)^3). - Bruno Berselli, Aug 11 2013