

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
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OFFSET

0,3


COMMENTS

Satisfies a(n+1) 2*a(n) + a(n1) = (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 to sequences with linear recurrences with constant coefficients, signature (2,1,1,2,1).


FORMULA

n^2  ceil[n(n1)/3]. G.f.: [x(1+2x^2x^3)]/[(1+x+x^2)(1x)^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 *)


CROSSREFS

Cf. A001082, A032766.
Sequence in context: A184747 A130258 A186496 * A192147 A226817 A154484
Adjacent sequences: A032762 A032763 A032764 * A032766 A032767 A032768


KEYWORD

nonn


AUTHOR

Patrick De Geest, May 15, 1998.


EXTENSIONS

Name change suggested by Wesley Ivan Hurt, Dec 20 2013


STATUS

approved



