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A081661 Partial sums of A081660. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 20 23:24 EST 2019. Contains 320362 sequences. (Running on oeis4.)