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A011849 a(n) = floor(binomial(n,3)/3). 3
0, 0, 0, 0, 1, 3, 6, 11, 18, 28, 40, 55, 73, 95, 121, 151, 186, 226, 272, 323, 380, 443, 513, 590, 674, 766, 866, 975, 1092, 1218, 1353, 1498, 1653, 1818, 1994, 2181, 2380, 2590, 2812, 3046, 3293, 3553, 3826 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,3,3,-6,3,3,-6,4,-1).

FORMULA

G.f.: x^4*(1-x+x^2)*(1-x^2+x^3)/((1-x)^3*(1-x^9)). - Ralf Stephan, Mar 05 2004

From R. J. Mathar, Apr 15 2010: (Start)

a(n) = 4*a(n-1) - 6*a(n-2) + 3*a(n-3) + 3*a(n-4) - 6*a(n-5) + 3*a(n-6) + 3*a(n-7) - 6*a(n-8) + 4*a(n-9) - a(n-10).

G.f.: x^4*(x^2-x+1)*(x^3-x^2+1) / ( (-1+x)^4*(x^6+x^3+1) ). (End)

a(n) = (1/54) * ( n^3 - 3*n - 6 + [6,8,4,-12,8,4,-30,8,4](mod 9) ). - Ralf Stephan, Aug 11 2013

MAPLE

seq(floor(binomial(n, 3)/3), n=0..42); # Zerinvary Lajos, Jan 12 2009

MATHEMATICA

CoefficientList[Series[x^4*(x^2-x+1)*(x^3-x^2+1)/((-1+x)^4*(x^6+x^3+1)), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 19 2012 *)

PROG

(MAGMA) [Floor(Binomial(n, 3)/3): n in [0..50]]; // Vincenzo Librandi, Jun 19 2012

CROSSREFS

A column of triangle A011857.

Sequence in context: A014125 A147456 A230088 * A173690 A178855 A095944

Adjacent sequences:  A011846 A011847 A011848 * A011850 A011851 A011852

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 23 07:30 EDT 2019. Contains 323508 sequences. (Running on oeis4.)