

A090023


Number of distinct lines through the origin in the ndimensional lattice of side length 7.


11



0, 1, 37, 415, 3745, 31471, 257257, 2078455, 16704865, 133935391, 1072633177, 8585561095, 68702163985, 549687102511, 4397773276297, 35183283965335, 281470638631105, 2251782504544831, 18014329402322617, 144114912035163175
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OFFSET

0,3


COMMENTS

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


LINKS

Table of n, a(n) for n=0..19.
Index entries for linear recurrences with constant coefficients, signature (18,115,330,424,192).


FORMULA

a(n) = 8^n  4^n  3^n  2^n + 2.
G.f.: x*(200*x^3136*x^2+19*x+1)/((x1)*(2*x1)*(3*x1)*(4*x1)*(8*x1)). [Colin Barker, Sep 04 2012]


EXAMPLE

a(2) = 37 because in 2D the lines have slope 0, 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[8^n  4^n  3^n  2^n + 2, {n, 0, 20}]


CROSSREFS

a(n) = T(n, 5) from A090030. Cf. A000225, A001047, A060867, A090020, A090021, A090022, A090024 are for dimension n with side lengths 1, 2, 3, 4, 5, 6, 8 respectively. A049691, A090025, A090026, A090027, A090028, A090029 are for side length k in 2, 3, 4, 5, 6, 7 dimensions.
Sequence in context: A201789 A115926 A083818 * A254682 A232251 A232259
Adjacent sequences: A090020 A090021 A090022 * A090024 A090025 A090026


KEYWORD

easy,nonn


AUTHOR

Joshua Zucker, Nov 20 2003


STATUS

approved



