A078098 -id:A078098 - cp's OEIS frontend

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

Benoit Cloitre, Dec 05 2002

nonn

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

Cf. A000196, A078109, A077623, A078098.

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

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))).

Original entry on oeis.org

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

Benoit Cloitre, Dec 05 2002

nonn

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)

Cf. A000196, A078108, A077623.

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

cp's OEIS Frontend

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))).

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