A106287 Number of orbits of the 5-step recursion mod n.

1, 8, 5, 96, 5, 56, 7, 1468, 203, 40, 11, 1312, 13, 56, 25, 23400, 17, 6392, 193, 480, 35, 88, 555, 37180, 2505, 104, 15539, 672, 293, 280, 151, 374292, 55, 136, 35, 199744, 37, 6128, 65, 7340, 41, 392, 1899, 1056, 1015, 6648, 313775, 627280, 14413, 20040, 85

Offset

1,2

Comments

Consider the 5-step recursion x(k)=x(k-1)+x(k-2)+x(k-3)+x(k-4)+x(k-5) mod n. For any of the n^5 initial conditions x(1), x(2), x(3), x(4) and x(5) in Zn, the recursion has a finite period. Each of these n^5 vectors belongs to exactly one orbit. In general, there are only a few different orbit lengths (A106290). For instance, the 1468 orbits mod 8 have lengths of 1, 2, 3, 6, 12 and 24.

Links

Table of n, a(n) for n=1..51.

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), A106286 (orbits of 4-step sequences), A106290 (number of different orbit lengths), A106309 (n producing a simple orbit structure).

Sequence in context: A317402 A317574 A195532 * A361711 A239862 A276688

Adjacent sequences: A106284 A106285 A106286 * A106288 A106289 A106290

Keyword

nonn

Author

T. D. Noe, May 02 2005

Status

approved