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