A181640 Partial sums of floor(n^2/5) (A118015).

0, 0, 0, 1, 4, 9, 16, 25, 37, 53, 73, 97, 125, 158, 197, 242, 293, 350, 414, 486, 566, 654, 750, 855, 970, 1095, 1230, 1375, 1531, 1699, 1879, 2071, 2275, 2492, 2723, 2968, 3227, 3500, 3788, 4092, 4412, 4748, 5100, 5469, 5856, 6261, 6684, 7125, 7585, 8065, 8565

Offset

0,5

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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,-3,1,0,1,-3,3,-1).

Formula

a(n) = Sum_{k=0..n} floor(k^2/5).

a(n) = round((2*n^3 + 3*n^2 - 11*n - 6)/30).

a(n) = floor((2*n^3 + 3*n^2 - 11*n + 6)/30).

a(n) = ceiling((2*n^3 + 3*n^2 - 11*n - 18)/30).

a(n) = a(n-5) + (n-2)^2, n > 4.

From Bruno Berselli, Dec 15 2010: (Start)

G.f.: x^3*(1+x)/((1 + x + x^2 + x^3 + x^4)*(1-x)^4).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-5) - 3*a(n-6) + 3*a(n-7) - a(n-8) for n > 7. (End)

Example

a(5) = 9 = 0 + 0 + 0 + 1 + 3 + 5.

Maple

a(n):=round((2*n^(3)+3*n^(2)-11*n-6)/(30))

Prog

(Magma) [Floor((2*n^3+3*n^2-11*n+6)/30): n in [0..50]]; // Vincenzo Librandi, May 01 2011

Crossrefs

Cf. A118015.

Sequence in context: A008086 A008087 A008088 * A033616 A265055 A011895

Adjacent sequences: A181637 A181638 A181639 * A181641 A181642 A181643

Keyword

nonn,easy

Author

Mircea Merca, Nov 18 2010

Status

approved