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

1,4

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).

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)

Mathematica

LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 0, 10, 41}, 50] (* Harvey P. Dale, Nov 18 2024 *)

Prog

(PARI) concat(vector(3), Vec(x^4*(10-9*x)/(1-x)^5 + O(x^50))) \\ Colin Barker, May 05 2016

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.

Sequence in context: A247201 A022278 A246972 * A006323 A178073 A102784

Adjacent sequences: A266393 A266394 A266395 * A266397 A266398 A266399

Keyword

nonn,easy

Author

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

Status

approved