

A087507


#{0<=k<=n: k*n is divisible by 3}.


4



1, 1, 1, 4, 2, 2, 7, 3, 3, 10, 4, 4, 13, 5, 5, 16, 6, 6, 19, 7, 7, 22, 8, 8, 25, 9, 9, 28, 10, 10, 31, 11, 11, 34, 12, 12, 37, 13, 13, 40, 14, 14, 43, 15, 15, 46, 16, 16, 49, 17, 17, 52, 18, 18, 55, 19, 19, 58, 20, 20, 61, 21, 21, 64, 22, 22, 67, 23, 23, 70, 24, 24, 73, 25, 25, 76
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


LINKS

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,1).


FORMULA

a(n) = sum{k=0..n, if (mod(kn, 3)=0, 1, 0) }.
a(n) = floor(n/3)(5/3+4/3cos(2Pi*/3))+1.
a(n)+A087508(n)+A087509(n) = n.
a(n) = 2*a(n3)a(n6) for n>5.  Colin Barker, May 02 2015
G.f.: (2*x^3+x^2+x+1) / ((x1)^2*(x^2+x+1)^2).  Colin Barker, May 02 2015


PROG

(PARI) Vec((2*x^3+x^2+x+1)/((x1)^2*(x^2+x+1)^2) + O(x^100)) \\ Colin Barker, May 02 2015


CROSSREFS

Cf. A016777 (trisection).
Sequence in context: A019834 A261557 A270809 * A020777 A153810 A098134
Adjacent sequences: A087504 A087505 A087506 * A087508 A087509 A087510


KEYWORD

easy,nonn


AUTHOR

Paul Barry, Sep 11 2003


STATUS

approved



