The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 range(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 AUTHOR Santi Spadaro, Jul 18 2001 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 16 06:48 EST 2021. Contains 340204 sequences. (Running on oeis4.)