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

0,2

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).

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

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 *)

Prog

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

Crossrefs

Cf. A001045, A081660.

Sequence in context: A295960 A068039 A188123 * A005103 A001978 A173283

Adjacent sequences: A081658 A081659 A081660 * A081662 A081663 A081664

Keyword

nonn,easy

Author

Paul Barry, Mar 26 2003

Status

approved