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A084570 Partial sums of A084263. 4
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 (list; graph; refs; listen; history; text; internal format)
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) = ceil(A006527(n+1) / 2).

a(n) = ceil((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

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Last modified May 26 03:51 EDT 2019. Contains 323579 sequences. (Running on oeis4.)