A078108 Let u(1)=u(2)=1, u(3)=2n, u(k) = abs(u(k-1)-u(k-2)-u(k-3)) and M(k)= Max( u(i) : 1<=i<=k), then for any k>=A078109(n), M(k)=sqrtint(k + a(n)) where sqrtint(x) denotes floor(sqrt(x)).

4, 24, 156, 184, 324, 608, 940, 1784, 1844, 3104, 5996, 4600, 4484, 6128, 6220, 7208, 8244, 9, 424, 11740, 13560, 14836, 19264, 19756, 23344, 24524, 26224, 32940, 34912, 34548, 42808, 52428, 46120, 47492, 52280, 67908, 86120, 8008, 4, 147152

Offset

1,1

Comments

It appears that (1) a(n) always exists, (2) a(n) is even, (3) a(n)/n^(5/2) -> infinity. If initial conditions are u(1)=u(2)=1, u(3)=2n+1, then u(k) reaches a 2-cycle for any k>m large enough (cf. A078098) - Benoit Cloitre, Jan 29 2006

Links

Table of n, a(n) for n=1..40.

Crossrefs

Cf. A000196, A078109, A077623.

Sequence in context: A003288 A178879 A091166 * A210474 A344735 A117337

Adjacent sequences: A078105 A078106 A078107 * A078109 A078110 A078111

Keyword

nonn

Author

Benoit Cloitre, Dec 05 2002

Status

approved