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Search: id:A104156
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| A104156 |
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a(1)=a(2)=0 then a(n)=abs(2*a(n-1)-a(n-2))-1. |
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+0
6
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| 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
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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A jumping flea sequence. The n-th jump is starting at indice 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 4-th jump : start with 4, then add (4-0)=4 to 4 which gives 8, then add (4-1)=3 to 8 giving 8+3=11, then 11+(4-2)=13, then 13+(4-3)=14. By symmetry you get the complete 4-th jump : {4,8,11,13,14,14,13,11,8,4}.
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FORMULA
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for any s>0 sum(k=s*(s+2), (s+1)*(s+3), a(k) )=1/3*(s+2)*(s+3)*(2*s-1)=2*A058373(s)
a(n) = (1/2)*(n-1-f(n+2)^2) where f(n)=floor(1/2+sqrt(n))-abs{n-1-floor(1/2+sqrt(n))^2} - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 17 2005
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PROGRAM
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(PARI) a(n)=if(n<3, 0, abs(2*a(n-1)-a(n-2))-1)
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CROSSREFS
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Sequence in context: A135229 A081372 A101489 this_sequence A070166 A131373 A034853
Adjacent sequences: A104153 A104154 A104155 this_sequence A104157 A104158 A104159
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KEYWORD
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sign
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 09 2005
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