A175848 Partial sums of ceiling(n^2/16).

0, 1, 2, 3, 4, 6, 9, 13, 17, 23, 30, 38, 47, 58, 71, 86, 102, 121, 142, 165, 190, 218, 249, 283, 319, 359, 402, 448, 497, 550, 607, 668, 732, 801, 874, 951, 1032, 1118, 1209, 1305, 1405, 1511, 1622, 1738, 1859, 1986, 2119, 2258, 2402, 2553, 2710

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Mircea Merca, Inequalities and Identities Involving Sums of Integer Functions J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,0,1,-3,3,-1).

Formula

a(n) = round((2*n+1)*(2*n^2 + 2*n + 51)/192);

a(n) = floor((2*n^3 + 3*n^2 + 52*n + 60)/96);

a(n) = ceiling((2*n^3 + 3*n^2 + 52*n - 9)/96);

a(n) = a(n-16) + (n+1)*(n-16) + 102.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-8) - 3*a(n-9) + 3*a(n-10) - a(n-11). - R. J. Mathar, Mar 11 2012

G.f.: x*(x^4 - x^3 + x^2 - x + 1)*(x^4 - x^2 + 1)/((x-1)^4*(x+1)*(x^2+1)*(x^4+1)). - Colin Barker, Oct 26 2012

Example

a(16) = 0+1+1+1+1+2+3+4+4+6+7+8+9+11+13+15+16 = 102.

Maple

seq(ceil((2*n^3+3*n^2+52*n-9)/96), n=0..50)

Mathematica

Accumulate[Ceiling[Range[0, 50]^2/16]]  (* Harvey P. Dale, Mar 04 2011 *)

Prog

(Magma) [Round((2*n+1)*(2*n^2+2*n+51)/192): n in [0..60]]; // Vincenzo Librandi, Jun 22 2011
(PARI) a(n)=(2*n^3+3*n^2+52*n+60)\96 \\ Charles R Greathouse IV, Jul 06 2017

Crossrefs

Sequence in context: A137446 A240028 A097557 * A240079 A240727 A123648

Adjacent sequences: A175845 A175846 A175847 * A175849 A175850 A175851

Keyword

nonn,easy

Author

Mircea Merca, Dec 05 2010

Status

approved