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A175724 Partial sums of floor(n^2/12). 1
0, 0, 0, 0, 1, 3, 6, 10, 15, 21, 29, 39, 51, 65, 81, 99, 120, 144, 171, 201, 234, 270, 310, 354, 402, 454, 510, 570, 635, 705, 780, 860, 945, 1035, 1131, 1233, 1341, 1455, 1575, 1701, 1834, 1974, 2121, 2275, 2436, 2604, 2780, 2964, 3156, 3356 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Partial sums of A008724.

LINKS

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

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

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^3+3*n^2-18*n)/72).

a(n) = a(n-6)+(n-2)*(n-3)/2, n>5.

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3)+a(n-6)-3*a(n-7)+3*a(n-8)-a(n-9), n>8.

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

MAPLE

A175724 := proc(n) add( floor(i^2/12) , i=0..n) ; end proc:

MATHEMATICA

Accumulate[Floor[Range[0, 49]^2/12]]

PROG

(MAGMA) [ &+[ Floor(j^2/12): j in [0..n] ]: n in [0..60] ];

CROSSREFS

Cf. A008724.

Sequence in context: A062099 A115650 A025745 * A101551 A227430 A051166

Adjacent sequences:  A175721 A175722 A175723 * A175725 A175726 A175727

KEYWORD

nonn,easy

AUTHOR

Mircea Merca, Aug 18 2010

STATUS

approved

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Last modified February 22 21:26 EST 2018. Contains 299469 sequences. (Running on oeis4.)