The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 31 05:53 EDT 2021. Contains 346367 sequences. (Running on oeis4.)