A173645 Partial sums of floor(n^2/11).

0, 0, 0, 0, 1, 3, 6, 10, 15, 22, 31, 42, 55, 70, 87, 107, 130, 156, 185, 217, 253, 293, 337, 385, 437, 493, 554, 620, 691, 767, 848, 935, 1028, 1127, 1232, 1343, 1460, 1584, 1715, 1853, 1998, 2150, 2310, 2478, 2654, 2838, 3030, 3230, 3439, 3657, 3884

Offset

0,6

Links

Bruno Berselli, Table of n, a(n) for n = 0..5000

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

Formula

a(n) = round((2*n^3 + 3*n^2 - 23*n - 12)/66).

a(n) = floor((2*n^3 + 3*n^2 - 23*n + 18)/66).

a(n) = ceiling((2*n^3 + 3*n^2 - 23*n - 42)/66).

a(n) = a(n-11) + (n-5)^2 + 6, n > 10.

From R. J. Mathar, Nov 24 2010: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-11) - 3*a(n-12) + 3*a(n-13) - a(n-14).

G.f.: x^4*(x+1)*(x^4 - x^3 + x^2 - x + 1) / ((x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x-1)^4). (End)

Example

a(6) = 6 = 0 + 0 + 0 + 0 + 1 + 2 + 3.

Maple

A173645(n):=round((2*n^3+3*n^2-23*n-12)/66)

Mathematica

Accumulate[Floor[Range[0, 50]^2/11]] (* Harvey P. Dale, Sep 23 2015 *)

Prog

(Magma) [ &+[Floor(k^2/11): k in [0..n]]: n in [0..60] ];  // Bruno Berselli, Apr 28 2011
(PARI) vector(60, n, n--; (2*n^3+3*n^2-23*n+18)\66) \\ G. C. Greubel, Jul 02 2019
(Sage) [floor((2*n^3+3*n^2-23*n+18)/66) for n in (0..60)] # G. C. Greubel, Jul 02 2019

Crossrefs

Sequence in context: A024918 A117245 A011914 * A122047 A177100 A265071

Adjacent sequences: A173642 A173643 A173644 * A173646 A173647 A173648

Keyword

nonn,easy

Author

Mircea Merca, Nov 24 2010

Status

approved