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_{i<=i<=k} u(i), then for any k >= A078109(n), M(k) = floor(sqrt(k + a(n))).

4, 24, 156, 184, 324, 608, 940, 1784, 1844, 3104, 5996, 4600, 4484, 6128, 6220, 7208, 8244, 9424, 11740, 13560, 14836, 19264, 19756, 23344, 24524, 26224, 32940, 34912, 34548, 42808, 52428, 46120, 47492, 52280, 67908, 86120, 80084, 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..38.

Crossrefs

Cf. A000196, A078109, A077623, A078098.

Sequence in context: A390358 A178879 A091166 * A210474 A344735 A117337

Adjacent sequences: A078105 A078106 A078107 * A078109 A078110 A078111

Keyword

nonn

Author

Benoit Cloitre, Dec 05 2002

Extensions

Typos in data corrected by Sean A. Irvine, Jun 16 2025

Status

approved