A266396 Number of orbits of Aut(Z^7) as function of the infinity norm n of the representative lattice point of the orbit, when the cardinality of the orbit is equal to 80640.
0, 0, 0, 10, 41, 105, 215, 385, 630, 966, 1410, 1980, 2695, 3575, 4641, 5915, 7420, 9180, 11220, 13566, 16245, 19285, 22715, 26565, 30866, 35650, 40950, 46800, 53235, 60291, 68005, 76415, 85560, 95480, 106216, 117810, 130305, 143745, 158175, 173641, 190190
Offset: 1
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Crossrefs
Programs
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Mathematica
LinearRecurrence[{5,-10,10,-5,1},{0,0,0,10,41},50] (* Harvey P. Dale, Nov 18 2024 *) -
PARI
concat(vector(3), Vec(x^4*(10-9*x)/(1-x)^5 + O(x^50))) \\ Colin Barker, May 05 2016
Formula
From Colin Barker, Dec 29 2015: (Start)
a(n) = (n^4+30*n^3-205*n^2+390*n-216)/24.
a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) for n>5.
G.f.: x^4*(10-9*x) / (1-x)^5.
(End)