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A077653 a(1)=1, a(2)=2, a(3)=2, a(n) = abs(a(n-1)-a(n-2)-a(n-3)). 6
1, 2, 2, 1, 3, 0, 4, 1, 3, 2, 2, 3, 1, 4, 0, 5, 1, 4, 2, 3, 3, 2, 4, 1, 5, 0, 6, 1, 5, 2, 4, 3, 3, 4, 2, 5, 1, 6, 0, 7, 1, 6, 2, 5, 3, 4, 4, 3, 5, 2, 6, 1, 7, 0, 8, 1, 7, 2, 6, 3, 5, 4, 4, 5, 3, 6, 2, 7, 1, 8, 0, 9, 1, 8, 2, 7, 3, 6, 4, 5, 5, 4, 6, 3, 7, 2, 8, 1, 9, 0, 10, 1, 9, 2, 8, 3, 7, 4, 6, 5, 5, 6, 4, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Conjecture : let z(1)=x; z(2)=y; z(3)= z; z(n)=abs(z(n-1)-z(n-2)-z(n-3)) if z(n) is unbounded (i.e. x,y,z are such that z(n) doesn't reach a cycle of length 2), then there are 2 integers n(x,y,z) and w(x,y,z) such that M(n) = floor(sqrt(n+w(x,y,z))) for n>n(,x,y,z) where M(n) = Max ( a(k) : 1<=k<=n ). As example : w(1,2,2)=9 n(1,2,2)=4; w(1,2,4)=29 n(1,2,4)=4; w(1,2,8)=157 n(1,2,8)=9

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n)/sqrt(n) is bounded. More precisely, let M(n) = Max ( a(k) : 1<=k<=n ); then M(n)= floor(sqrt(n+9)) for n>4

PROG

(Haskell)

a077653 n = a077653_list !! (n-1)

a077653_list = 1 : 2 : 2 : zipWith3 (\u v w -> abs (w - v - u))

               a077653_list (tail a077653_list) (drop 2 a077653_list)

-- Reinhard Zumkeller, Oct 11 2014

CROSSREFS

Cf. A077623, A079623, A079624, A080096, A088226.

Sequence in context: A294076 A117046 A268192 * A077889 A305805 A230260

Adjacent sequences:  A077650 A077651 A077652 * A077654 A077655 A077656

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Dec 02 2002

STATUS

approved

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Last modified April 19 04:19 EDT 2019. Contains 322237 sequences. (Running on oeis4.)