This site is supported by donations to The OEIS 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!)
 A130518 a(n) = Sum_{k=0..n} floor(k/3). (Partial sums of A002264.) 17
 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, 408, 425, 442, 459, 477, 495, 513, 532, 551, 570 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Complementary with A130481 regarding triangular numbers, in that A130481(n)+3*a(n) = n(n+1)/2 = A000217(n). Apart from offset, the same as A062781. - R. J. Mathar, Jun 13 2008 Apart from offset, the same as A001840. - Michael Somos, Sep 18 2010 The sum of any three consecutive terms is a triangular number. - J. M. Bergot, Nov 27 2014 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1). FORMULA G.f.: x^3 / ((1-x^3)*(1-x)^2). a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5). a(n) = (1/2)*floor(n/3)*(2n-1-3*floor(n/3)))) = A002264(n)*(2n-1-3*A002264(n))/2. a(n) = (1/2)*A002264(n)*(n-1+A010872(n)). a(n) = round(n*(n-1)/6) = round((n^2-n-1)/6) = floor(n*(n-1)/6) = ceil((n+1)*(n-2)/6). [Mircea Merca, Nov 28 2010] a(n) = a(n-3)+n-2, n>2. [Mircea Merca, Nov 28 2010] a(n) = A214734(n, 1, 3). [Renzo Benedetti, Aug 27 2012] a(3n) = A000326(n), a(3n+1) = A005449(n), a(3n+2) = 3*A000217(n) = A045943(n). - Philippe Deléham, Mar 26 2013 a(n) = ( 3*n*(n-1) - (-1)^n*( (1+i*sqrt(3))^(n-2)+(1-i*sqrt(3))^(n-2) )/2^(n-3) - 2 )/18, where i=sqrt(-1). [Bruno Berselli, Nov 30 2014] MAPLE seq(floor(n*(n-1)/6), n=0..100); # Robert Israel, Nov 27 2014 MATHEMATICA Table[n, {n, 0, 19}, {3}] // Flatten // Accumulate (* Jean-François Alcover, Jun 05 2013 *) PROG (Sage) [floor(binomial(n, 2)/3) for n in xrange(0, 60)] # [Zerinvary Lajos, Dec 01 2009] (MAGMA) [Round(n*(n-1)/6): n in [0..60]]; // Vincenzo Librandi, Jun 25 2011 (PARI) a(n)=n*(n-1)\/6 \\ Charles R Greathouse IV, Jun 05 2013 CROSSREFS Cf. A002265, A002266, A004526, A010872, A010873, A010874, A062781, A130482, A130483. Sequence in context: A062781 A145919 A058937 * A001840 A022794 A025693 Adjacent sequences:  A130515 A130516 A130517 * A130519 A130520 A130521 KEYWORD nonn,easy AUTHOR Hieronymus Fischer, Jun 01 2007 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 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)