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A090022
Number of distinct lines through the origin in the n-dimensional lattice of side length 6.
12
0, 1, 25, 253, 2065, 15541, 112825, 804973, 5692705, 40071781, 281367625, 1972955293, 13823978545, 96820307221, 677949854425, 4746473419213, 33228592555585, 232613204977861, 1628344491013225, 11398619145204733
OFFSET
0,3
COMMENTS
Equivalently, lattice points where the gcd of all the coordinates is 1.
LINKS
FORMULA
a(n) = 7^n - 4^n - 3^n + 1.
O.g.f.: 1/(-1+3*x) + 1/(-1+4*x) - 1/(-1+x) - 1/(-1+7*x). - R. J. Mathar, Feb 26 2008
EXAMPLE
a(2) = 25 because in 2D the lines have slope 0, 1/6, 5/6, 1/5, 2/5, 3/5, 4/5, 1/4, 3/4, 1/3, 2/3, 1/2, 1 and their reciprocals.
MATHEMATICA
Table[7^n - 4^n - 3^n + 1, {n, 0, 25}]
PROG
(Python) [7**n-4**n-3**n+1 for n in range(20)] # Gennady Eremin, Mar 06 2022
(Magma) [7^n-4^n-3^n+1: n in [0..20]]; // Wesley Ivan Hurt, Mar 06 2022
CROSSREFS
a(n) = T(n, 5) from A090030. Cf. A000225, A001047, A060867, A090020, A090021, A090023, A090024 are for dimension n with side lengths 1, 2, 3, 4, 5, 7, 8 respectively. A049691, A090025, A090026, A090027, A090028, A090029 are for side length k in 2, 3, 4, 5, 6, 7 dimensions.
Sequence in context: A308492 A042208 A143009 * A298068 A017450 A264267
KEYWORD
easy,nonn
AUTHOR
Joshua Zucker, Nov 20 2003
STATUS
approved