A106286 Number of orbits of the 4-step recursion mod n.

1, 4, 6, 28, 3, 24, 10, 220, 91, 12, 130, 240, 343, 40, 168, 1756, 19, 364, 22, 132, 81, 2068, 26, 1968, 253, 1372, 2336, 448, 2557, 672, 16, 14044, 1143, 76, 108, 4612, 1411, 88, 3084, 1860, 11815, 324, 22, 32092, 13213, 104, 50, 15792, 2467, 4012, 168, 17812

Offset

1,2

Comments

Consider the 4-step recursion x(k)=x(k-1)+x(k-2)+x(k-3)+x(k-4) mod n. For any of the n^4 initial conditions x(1), x(2), x(3) and x(4) in Zn, the recursion has a finite period. Each of these n^4 vectors belongs to exactly one orbit. In general, there are only a few different orbit lengths (A106289) for each n. For instance, the 220 orbits mod 8 have lengths of 1, 5, 10 and 20.

Links

Table of n, a(n) for n=1..52.

D. D. Wall, Fibonacci series modulo m, Amer. Math. Monthly, 67 (1960), 525-532.

Eric Weisstein's World of Mathematics, Fibonacci n-Step Number.

Crossrefs

Cf. A015134 (orbits of Fibonacci sequences), A106285 (orbits of 3-step sequences), A106287 (orbits of 5-step sequences), A106289 (number of different orbit lengths), A106308 (n producing a simple orbit structure).

Sequence in context: A349647 A012896 A013078 * A066293 A204385 A341045

Adjacent sequences: A106283 A106284 A106285 * A106287 A106288 A106289

Keyword

nonn

Author

T. D. Noe, May 02 2005

Status

approved