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

Author

Paul Barry, Mar 26 2003

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A001045, A081660.

Programs

Magma

[2^(n+2)/3+(n^2+n-1)/2+(-1)^n/6: n in [0..40]]; // Vincenzo Librandi, Aug 10 2013

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

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