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A160378 a(n) = n^3 - n*(n+1)/2. 7
0, 0, 5, 21, 54, 110, 195, 315, 476, 684, 945, 1265, 1650, 2106, 2639, 3255, 3960, 4760, 5661, 6669, 7790, 9030, 10395, 11891, 13524, 15300, 17225, 19305, 21546, 23954, 26535, 29295, 32240, 35376, 38709, 42245, 45990, 49950, 54131, 58539 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

n-th cube (A000578(n)) minus n-th triangular number (A000217(n)).

Partial sums of A045944. - Vladimir Joseph Stephan Orlovsky, Jun 25 2009

The sum of the n-1 numbers between n^2 and n*(n+1) = a(n). - J. M. Bergot, Apr 15 2013

Use the terms in A061885 to form the antidiagonals for an array. The antidiagonals begin: 0;2,3;6,7,8;12,13,14,15;20,21,22,23,24,25.  The sum of the terms in these antidiagonals = a(n)for n > 0. - J. M. Bergot, Jul 08 2013

a(n) is the sum of the n numbers strictly between n^2-n-1 and n^2. - Charlie Marion, Feb 21 2020

LINKS

Table of n, a(n) for n=0..39.

M. Janjic and B. Petkovic, A counting function, arXiv preprint arXiv:1301.4550 [math.CO], 2013.

FORMULA

a(n) = (2*n^3 - n^2 - n)/2. - Vincenzo Librandi, Dec 12 2010; edited by Klaus Brockhaus, Dec 12 2010

EXAMPLE

a(4) = 4^3 - 4*5/2 = 64 - 10 = 54.

MATHEMATICA

f[n_]:=6*n+5; s1=s2=0; lst={}; Do[a=f[n]; s1+=a; s2+=s1; AppendTo[lst, s2], {n, 0, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jun 25 2009 *)

Table[Sum[(n^2 - i), {i, 1, n}], {n, 1, 36}] (* Zerinvary Lajos, Jul 11 2009 *)

PROG

(MAGMA) [ n^3-n*(n+1)/2: n in [0..50] ];

CROSSREFS

Cf. A000578, A000217, A045944.

Sequence in context: A219219 A272810 A147834 * A201440 A096942 A122244

Adjacent sequences:  A160375 A160376 A160377 * A160379 A160380 A160381

KEYWORD

nonn

AUTHOR

Gil Broussard, May 11 2009

EXTENSIONS

Definition clarified and offset changed from 1 to 0 by Klaus Brockhaus, Dec 12 2010

STATUS

approved

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Last modified May 14 22:40 EDT 2021. Contains 343909 sequences. (Running on oeis4.)