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

Author

Philippe A.J.G. Chevalier, Dec 29 2015

Keywords

• nonn
• easy

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

Number of orbits of Aut(Z^7) as function of the infinity norm A000579, A154286, A102860, A002412, A045943, A115067, A008586, A008585, A005843, A001477, A000217.

Programs

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)