A078109 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_{1<=i<=k} u(i), then for any k >= a(n), M(k) = floor(sqrt(k + A078108(n))).

3, 10, 38, 10, 35, 66, 19, 150, 90, 30, 243, 159, 138, 270, 19, 186, 35, 178, 358, 127, 46, 334, 123, 370, 438, 343, 182, 430, 46, 454, 470, 534, 30, 618, 734, 903, 570, 302, 571, 638, 30, 166, 822, 647, 426, 998, 75, 106, 606, 322, 82, 210, 1798, 330, 506

Offset: 1

Author

Benoit Cloitre, Dec 05 2002

Keywords

• nonn

Comments

Conjecture : a(n) always exists, a(n)/n^2 is bounded. 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)

Crossrefs

Cf. A000196, A078108, A077623.

Extensions

Typos in data corrected and more terms from Sean A. Irvine, Jun 16 2025