A084570 Partial sums of A084263.

1, 2, 6, 12, 23, 38, 60, 88, 125, 170, 226, 292, 371, 462, 568, 688, 825, 978, 1150, 1340, 1551, 1782, 2036, 2312, 2613, 2938, 3290, 3668, 4075, 4510, 4976, 5472, 6001, 6562, 7158, 7788, 8455, 9158, 9900, 10680, 11501, 12362, 13266, 14212, 15203, 16238

Offset

0,2

Comments

Partial sums give A084569.

Links

Table of n, a(n) for n=0..45.

Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

Formula

a(n) = (-1)^n/4 + (2n^3 + 6n^2 + 10n + 9)/12.

a(n) = Sum_{j=0..n} (Sum_{i=0..j} (i + (-1)^i)).

From Arun Giridhar, Apr 03 2015: (Start)

a(n) = ceiling(A006527(n+1) / 2).

a(n) = ceiling((n^3 + 3n^2 + 5n + 3)/6).

(End)

G.f.: (1-x+2*x^2)/((1+x)*(1-x)^4). - Vincenzo Librandi, Apr 04 2015

Mathematica

LinearRecurrence[{3, -2, -2, 3, -1}, {1, 2, 6, 12, 23}, 50] (* Harvey P. Dale, Nov 12 2014 *)
CoefficientList[Series[(1 - x + 2 x^2) / ((1 + x) (1 - x)^4), {x, 0, 50}], x] (* Vincenzo Librandi, Apr 04 2015 *)

Prog

(PARI) a(n) = sum(j=0, n, sum(i=0, j, (i+(-1)^i)));
vector(50, n, n--; a(n)) \\ Michel Marcus, Apr 04 2015
(Magma) [(-1)^n/4 + (2*n^3+6*n^2+10*n+ 9)/12: n in [0..50]]; // Vincenzo Librandi, Apr 04 2015

Crossrefs

Sequence in context: A131520 A086953 A101953 * A069956 A062476 A192703

Adjacent sequences: A084567 A084568 A084569 * A084571 A084572 A084573

Keyword

easy,nonn

Author

Paul Barry, May 31 2003

Status

approved