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A062781 Number of arithmetic progressions of four terms and any mean which can be extracted from the set of the first n positive integers. 3
0, 0, 0, 1, 2, 3, 5, 7, 9, 12, 15, 18, 22, 26, 30, 35, 40, 45, 51, 57, 63, 70, 77, 84, 92, 100, 108, 117, 126, 135, 145, 155, 165, 176, 187, 198, 210, 222, 234, 247, 260, 273, 287, 301, 315, 330, 345, 360, 376, 392 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

This sequence seems to be a shifted version of the Somos sequence A058937.

Equal to the partial sums of A002264 (cf. A130518) but with initial index 1 instead of 0. - Hieronymus Fischer, Jun 01 2007

Apart from offset, the same as A130518. - R. J. Mathar, Jun 13 2008

Apart from offset, the same as A001840. - Michael Somos, Sep 18 2010

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..750

M. Somos, Somos Polynomials

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

FORMULA

a(n) = P(n,4), where P(n,k) = n*floor(n/(k - 1)) - (1/2)(k - 1)(floor(n/(k - 1))*(floor(n/(k - 1)) + 1)); recursion: a(n) = a(n-3) + n - 3; a(1) = a(2) = a(3) = 0.

From Hieronymus Fischer, Jun 01 2007: (Start)

a(n) = (1/2)*floor((n-1)/3)*(2*n - 3 - 3*floor((n-1)/3)).

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

a(n) = floor((n-1)/3) + a(n-1). - Jon Maiga, Nov 25 2018

E.g.f.: ((4 - 6*x + 3*x^2)*exp(x) - 4*exp(-x/2)*cos(sqrt(3)*x/2))/18. - Franck Maminirina Ramaharo, Nov 25 2018

MAPLE

seq(coeff(series(x^4/((1-x^3)*(1-x)^2), x, n+1), x, n), n = 1 .. 50); # Muniru A Asiru, Nov 25 2018

MATHEMATICA

RecurrenceTable[{a[0]==0, a[n]==Floor[n/3] + a[n-1]}, a, {n, 49}] (* Jon Maiga, Nov 25 2018 *)

PROG

(Sage) [floor(binomial(n, 2)/3) for n in xrange(0, 50)] # Zerinvary Lajos, Dec 01 2009

CROSSREFS

Cf. A058937, A001840.

Cf. A002620, A130519, A130520.

Sequence in context: A024195 A071423 A211004 * A145919 A058937 A130518

Adjacent sequences:  A062778 A062779 A062780 * A062782 A062783 A062784

KEYWORD

nonn,easy,changed

AUTHOR

Santi Spadaro, Jul 18 2001

STATUS

approved

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Last modified November 18 17:57 EST 2019. Contains 329288 sequences. (Running on oeis4.)