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 A106287 Number of orbits of the 5-step recursion mod n. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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. REFERENCES D. D. Wall, Fibonacci series modulo m, Amer. Math. Monthly, Vol. 67, 1960, 525-532. LINKS Eric Weisstein's World of Mathematics, Fibonacci n-Step 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: A213841 A038283 A195532 * A010117 A010119 A010116 Adjacent sequences:  A106284 A106285 A106286 * A106288 A106289 A106290 KEYWORD nonn AUTHOR T. D. Noe, May 02 2005 STATUS approved

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