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A078617 Floor(average of first n squares). 6
1, 2, 4, 7, 11, 15, 20, 25, 31, 38, 46, 54, 63, 72, 82, 93, 105, 117, 130, 143, 157, 172, 188, 204, 221, 238, 256, 275, 295, 315, 336, 357, 379, 402, 426, 450, 475, 500, 526, 553, 581, 609, 638, 667, 697, 728, 760, 792, 825, 858, 892, 927, 963, 999, 1036, 1073 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..56.

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,1,-2,1)

FORMULA

a(n) = floor((1/n)(Sum_{i=1, ..., n} i^2) = floor( A000330(n)/n ).

a(n) = [(n + 1) * (2 * n + 1) / 6]. A171662(n) = a(-1 - n). - Michael Somos, Dec 14 2009

G.f. -x*(1+x^3+x^4+x^2) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^3 ). - R. J. Mathar, Feb 20 2011

a(n) = floor(n/(1-e^(-3/n))). Also see related exponential formula in A171662 with symmetry as above. - Richard R. Forberg, Jun 22 2013

EXAMPLE

a(4) = Floor((1 + 4 + 9 + 16)/4) = 7.

MAPLE

BB:=n->sum(i^2, i=1..n): a:=n->floor(numer(BB(n))/n): seq(a(n), n=1..56); # Zerinvary Lajos, Mar 28 2007

MATHEMATICA

s = 0; a = {}; For[i = 1, i <= 100, i++, s = s + i^2; a = Append[a, Floor[(1/i) s]]]; a

PROG

(PARI) {a(n) = n++; (2 * n^2 - n) \ 6} /* Michael Somos, Dec 14 2009 */

CROSSREFS

Sequence in context: A003068 A194168 A198759 * A199085 A247184 A025703

Adjacent sequences:  A078614 A078615 A078616 * A078618 A078619 A078620

KEYWORD

easy,nonn

AUTHOR

Joseph L. Pe, Dec 10 2002

STATUS

approved

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Last modified May 31 22:45 EDT 2020. Contains 334756 sequences. (Running on oeis4.)