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A102396
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A mod 2 related Jacobsthal sequence.
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2
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0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 3, 3, 5, 1, 1, 1, 3, 1, 3, 3, 5, 1, 3, 3, 5, 3, 5, 5, 11, 1, 1, 1, 3, 1, 3, 3, 5, 1, 3, 3, 5, 3, 5, 5, 11, 1, 3, 3, 5, 3, 5, 5, 11, 3, 5, 5, 11, 5, 11, 11, 21, 1, 1, 1, 3, 1, 3, 3, 5, 1, 3, 3, 5, 3, 5, 5, 11, 1, 3, 3, 5, 3, 5, 5, 11, 3, 5, 5, 11, 5, 11, 11, 21, 1, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| a(2^n-1)=A001045(n). Conjecture : all elements a(n) are Jacobsthal numbers. A001316(n)=A102395(n)+2*A102396(n).
The conjecture is true since a(n)=A001045(A000120(n)). - Paul Barry (pbarry(AT)wit.ie), Jan 07 2005
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FORMULA
| a(n)=sum{k=0..n, if(mod(n+k, 3)=1, C(n, k) mod 2, 0)}; a(n)=sum{k=0..n, if(mod(n+k, 3)=2, C(n, k) mod 2, 0)}.
a(n)=(1/2)*sum(k=0, n, {F(n+k)*binomial(n, k)} mod 2) where F=A000045; recurrence : a(0)=0 then a(2n)=a(n) and a(2n+1)=2*a(n)+1-2*t(n) where t(n)=A010060(n) is the Thue-Morse sequence - Benoit Cloitre (benoit7848c(AT)orange.fr), May 15 2005
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CROSSREFS
| Sequence in context: A095345 A132468 A090176 * A095960 A183093 A183096
Adjacent sequences: A102393 A102394 A102395 * A102397 A102398 A102399
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jan 06 2005
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