

A104156


a(1)=a(2)=0, a(n) = abs(2*a(n1)  a(n2))  1.


5



0, 0, 1, 1, 2, 2, 1, 1, 2, 4, 5, 5, 4, 2, 1, 3, 6, 8, 9, 9, 8, 6, 3, 1, 4, 8, 11, 13, 14, 14, 13, 11, 8, 4, 1, 5, 10, 14, 17, 19, 20, 20, 19, 17, 14, 10, 5, 1, 6, 12, 17, 21, 24, 26, 27, 27, 26, 24, 21, 17, 12, 6, 1, 7, 14, 20, 25, 29, 32, 34, 35, 35, 34, 32, 29, 25, 20, 14, 7, 1, 8, 16, 23, 29, 34, 38, 41, 43, 44, 44, 43, 41, 38, 34, 29, 23
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OFFSET

1,5


COMMENTS

A jumping flea sequence. The nth jump is starting at index n(n+2) and is ending at (n+1)(n+3). It reaches the altitude of n(n+3)/2 and can be given directly (omitting the 1's). For instance, for the 4th jump: start with 4, then add (40)=4 to 4 which gives 8, then add (41)=3 to 8 giving 8+3=11, then 11+(42)=13, then 13+(43)=14. By symmetry you get the complete 4th jump: {4,8,11,13,14,14,13,11,8,4}.


LINKS

Table of n, a(n) for n=1..96.


FORMULA

for any s>0 sum(k=s*(s+2), (s+1)*(s+3), a(k) )=1/3*(s+2)*(s+3)*(2*s1)=2*A058373(s).
a(n) = (1/2)*(n1f(n+2)^2) where f(n)=floor(1/2+sqrt(n))abs{n1floor(1/2+sqrt(n))^2}.  Benoit Cloitre, Mar 17 2005


PROG

(PARI) a(n)=if(n<3, 0, abs(2*a(n1)a(n2))1)


CROSSREFS

Sequence in context: A257543 A081372 A101489 * A070166 A131373 A245185
Adjacent sequences: A104153 A104154 A104155 * A104157 A104158 A104159


KEYWORD

sign


AUTHOR

Benoit Cloitre, Mar 09 2005


STATUS

approved



