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A090021 Number of distinct lines through the origin in the n-dimensional lattice of side length 5. 11
0, 1, 21, 175, 1185, 7471, 45801, 277495, 1672545, 10056991, 60405081, 362615815, 2176242705, 13059083311, 78359348361, 470170570135, 2821066729665, 16926530042431, 101559568723641, 609358576700455, 3656154951181425 (list; graph; refs; listen; history; text; internal format)
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..20.

Index entries for linear recurrences with constant coefficients, signature (12,-47,72,-36).

FORMULA

a(n) = 6^n - 3^n - 2*2^n + 2.

G.f.: -x*(30*x^2-9*x-1)/((x-1)*(2*x-1)*(3*x-1)*(6*x-1)). [Colin Barker, Sep 04 2012]

EXAMPLE

a(2) = 21 because in 2D the lines have slope 0, 1/5, 2/5, 3/5, 4/5, 1/4, 3/4, 1/3, 2/3, 1/2, 1 and their reciprocals.

MATHEMATICA

Table[6^n - 3^n - 2*2^n + 2, {n, 0, 25}]

LinearRecurrence[{12, -47, 72, -36}, {0, 1, 21, 175}, 30] (* Harvey P. Dale, Jul 18 2016 *)

CROSSREFS

a(n) = T(n, 5) from A090030. Cf. A000225, A001047, A060867, A090020, A090022, A090023, A090024 are for dimension n with side lengths 1, 2, 3, 4, 6, 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: A119105 A015880 A113163 * A254681 A219625 A244875

Adjacent sequences:  A090018 A090019 A090020 * A090022 A090023 A090024

KEYWORD

easy,nonn

AUTHOR

Joshua Zucker, Nov 19 2003

STATUS

approved

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Last modified November 21 22:16 EST 2019. Contains 329383 sequences. (Running on oeis4.)