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A032765 Floor(n(n+1)(n+2) / (n+ n+1 + n+2)), which equals floor(n(n + 2)/3). 16
0, 1, 2, 5, 8, 11, 16, 21, 26, 33, 40, 47, 56, 65, 74, 85, 96, 107, 120, 133, 146, 161, 176, 191, 208, 225, 242, 261, 280, 299, 320, 341, 362, 385, 408, 431, 456, 481, 506, 533, 560, 587, 616, 645, 674, 705, 736, 767, 800, 833, 866, 901, 936, 971, 1008 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Satisfies a(n+1) -2*a(n) + a(n-1) = (2/3)(1+w^(n+1)+w^(2n+2)), a(0)=0 & a(1)=1 where w is the imaginary cubic root of unity. - Robert G. Wilson v, Jun 24 2002

First differences have this pattern: (+1) +1 +1 +3 +3 +3 +5 +5 +5 +7 +7 +7 +9 +9 +9. - Alexandre Wajnberg, Dec 19 2005

LINKS

Table of n, a(n) for n=0..54.

J. Bader, Kobon Triangles

Gilles Clement and Johannes Bader, Tighter Upper Bound for the Number of Kobon Triangles, Unpublished, 2007

Gilles Clement and Johannes Bader, Tighter Upper Bound for the Number of Kobon Triangles, Unpublished, 2007 [Cached copy, with permission]

Eric Weisstein's World of Mathematics, Kobon Triangle

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

FORMULA

n^2 - ceil[n(n-1)/3]. G.f.: [x(1+2x^2-x^3)]/[(1+x+x^2)(1-x)^3]. - Ralf Stephan, May 05 2004

a(n) = Floor [n(n+2)/3]. - Saburo Tamura, sent by Alexandre Wajnberg, Dec 19 2005

MAPLE

A032765:=n->floor(n*(n+2)/3); seq(A032765(n), n=0..100); # Wesley Ivan Hurt, Dec 20 2013

MATHEMATICA

Table[ Floor[ n(n + 1)(n + 2)/(n + (n + 1) + (n + 2))], {n, 0, 55}]

Table[Floor[n (n + 2)/3], {n, 0, 100}] (* Wesley Ivan Hurt, Dec 20 2013 *)

LinearRecurrence[{2, -1, 1, -2, 1}, {0, 1, 2, 5, 8}, 60] (* Harvey P. Dale, Jun 06 2016 *)

PROG

(PARI) a(n)=n*(n+2)\3 \\ Charles R Greathouse IV, Jun 11 2015

CROSSREFS

Cf. A001082, A032766.

Sequence in context: A184747 A130258 A186496 * A261416 A192147 A226817

Adjacent sequences:  A032762 A032763 A032764 * A032766 A032767 A032768

KEYWORD

nonn,easy

AUTHOR

Patrick De Geest, May 15 1998

EXTENSIONS

Name change suggested by Wesley Ivan Hurt, Dec 20 2013

STATUS

approved

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Last modified December 4 19:20 EST 2016. Contains 278755 sequences.