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A032765 Floor(n(n+1)(n+2) / (n+ n+1 + n+2)), which equals floor(n(n + 2)/3). 15
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.

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 *)

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 August 28 22:18 EDT 2015. Contains 261164 sequences.