

A090024


Number of distinct lines through the origin in the ndimensional lattice of side length 8.


12



0, 1, 45, 571, 5841, 55651, 515025, 4702531, 42649281, 385447171, 3476958705, 31332052291, 282184860321, 2540643522691, 22870684139985, 205860600134851, 1852867557848961, 16676418630942211, 150090820212050865
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OFFSET

0,3


COMMENTS

Equivalently, lattice points where the gcd of all the coordinates is 1.


LINKS

Gennady Eremin, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (20,140,430,579,270).


FORMULA

a(n) = 9^n  5^n  3^n  2^n + 2.
G.f.: x*(291*x^3189*x^2+25*x+1)/((x1)*(2*x1)*(3*x1)*(5*x1)*(9*x1)). [Colin Barker, Sep 04 2012]


EXAMPLE

a(2) = 45 because in 2D the lines have slope 0, 1/8, 3/8, 5/8, 7/8, 1/7, 2/7, 3/7, 4/7, 5/7, 6/7, 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[9^n  5^n  3^n  2^n + 2, {n, 0, 20}]


PROG

(Python)
[9**n5**n3**n2**n+2 for n in range(30)] # Gennady Eremin, Mar 12 2022


CROSSREFS

a(n) = T(n, 5) from A090030. Cf. A000225, A001047, A060867, A090020, A090021, A090022, A090023 are for dimension n with side lengths 1, 2, 3, 4, 5, 6, 7 respectively. A049691, A090025, A090026, A090027, A090028, A090029 are for side length k in 2, 3, 4, 5, 6, 7 dimensions.
Sequence in context: A160837 A160838 A189350 * A282767 A160234 A110691
Adjacent sequences: A090021 A090022 A090023 * A090025 A090026 A090027


KEYWORD

easy,nonn


AUTHOR

Joshua Zucker, Nov 20 2003


STATUS

approved



