

A102899


a(n) = ceiling(n/3)^2  floor(n/3)^2.


2



0, 1, 1, 0, 3, 3, 0, 5, 5, 0, 7, 7, 0, 9, 9, 0, 11, 11, 0, 13, 13, 0, 15, 15, 0, 17, 17, 0, 19, 19, 0, 21, 21, 0, 23, 23, 0, 25, 25, 0, 27, 27, 0, 29, 29, 0, 31, 31, 0, 33, 33, 0, 35, 35, 0, 37, 37, 0, 39, 39, 0, 41, 41, 0, 43, 43, 0, 45, 45, 0, 47, 47, 0, 49, 49, 0, 51, 51, 0, 53, 53, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,5


REFERENCES

Maria Paola Bonacina and Nachum Dershowitz, Canonical Inference for Implicational Systems, in Automated Reasoning, Lecture Notes in Computer Science, Volume 5195/2008, SpringerVerlag.


LINKS

Table of n, a(n) for n=0..81.
Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,1)


FORMULA

G.f.: x(1+x+x^3+x^4)/(12x^3+x^6);
a(n) = A011655(n)*A004396(n).
a(n) = floor((2n+1)/3)*(2/3)*(1cos(2*Pi*n/3)).
a(n) = A120691(n+1) for n>0; a(n) = ([n/3]*2+1)*dist(n,3Z).  M. F. Hasler, Dec 13 2007
a(n) = 2*sin(n*Pi/3)*(4*n*sin(n*Pi/3)sqrt(3)*cos(n*Pi))/9.  Wesley Ivan Hurt, Sep 24 2017


PROG

(PARI) A102899(n)=(n\3*2+1)*(0<n%3) \\ M. F. Hasler, Dec 13 2007


CROSSREFS

Cf. A003417, A120691.
Sequence in context: A256119 A217552 A128046 * A072689 A021972 A193451
Adjacent sequences: A102896 A102897 A102898 * A102900 A102901 A102902


KEYWORD

easy,nonn


AUTHOR

Paul Barry, Jan 17 2005


STATUS

approved



