A175780 Partial sums of floor(n^2/24).

0, 0, 0, 0, 0, 1, 2, 4, 6, 9, 13, 18, 24, 31, 39, 48, 58, 70, 83, 98, 114, 132, 152, 174, 198, 224, 252, 282, 314, 349, 386, 426, 468, 513, 561, 612, 666, 723, 783, 846, 912, 982, 1055, 1132, 1212, 1296, 1384, 1476, 1572, 1672, 1776

Offset

0,7

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.

Formula

a(n) = round((2*n+1)*(2*n^2 + 2*n - 37)/288).

a(n) = floor((2*n+11)*(n-2)^2/144).

a(n) = ceiling((2*n-9)*(n+3)^2/144).

a(n) = a(n-24) + (n+1)*(n-24) + 198, n > 23.

G.f.: x^5*(1 - x + x^2 - x^3 + x^4) / ( (1+x)*(1+x^2)*(x^4-x^2+1)*(x^2-x+1)*(1+x+x^2)*(x-1)^4 ). - R. J. Mathar, Dec 06 2010

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-12) - 3*a(n-13) + 3*a(n-14) - a(n-15). - R. J. Mathar, Dec 06 2010

Example

a(24) = 0 + 0 + 0 + 0 + 0 + 1 + 1 + 2 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 12 + 13 + 15 + 16 + 18 + 20 + 22 + 24 = 198.

Maple

seq(ceil((2*n-9)*(n+3)^2/144), n=0..50)

Prog

(Magma) [Round((2*n+1)*(2*n^2+2*n-37)/288): n in [0..60]]; // Vincenzo Librandi, Jun 22 2011

Crossrefs

Cf. A175777.

Sequence in context: A079717 A247179 A319158 * A114830 A177239 A001304

Adjacent sequences: A175777 A175778 A175779 * A175781 A175782 A175783

Keyword

nonn,easy

Author

Mircea Merca, Dec 04 2010

Status

approved