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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
OFFSET
0,2
COMMENTS
Partial sums give A084569.
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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 31 2003
STATUS
approved