A103157 - OEIS

A103157

Number of ways to choose 4 distinct points from an (n+1) X (n+1) X (n+1) lattice cube.

70, 17550, 635376, 9691375, 88201170, 566685735, 2829877120, 11671285626, 41417124750, 130179173740, 370215608400, 968104633665, 2357084537626, 5396491792125, 11710951848960, 24246290643940, 48151733324310, 92140804597626, 170538695998000, 306294282269955

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OFFSET

1,1

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

FORMULA

a(n) = binomial((n+1)^3, 4).

G.f.: -x*(x^10 + 317*x^9 + 23193*x^8 + 435669*x^7 + 2747685*x^6 + 6738399*x^5 + 6803373*x^4 + 2780367*x^3 + 412686*x^2 + 16640*x + 70)/(x -1)^13. - Colin Barker, Nov 16 2012

CROSSREFS

Cf. 4-point objects in lattice cube: A103158 tetrahedra, A103656 triangular pyramids, A103657 number of different volumes, A103658 volume=0, A103659, A103660 most frequent volumes, A103661 smallest not occurring volume.

Sequence in context: A362169 A231054 A007100 * A364305 A007099 A004109

Adjacent sequences: A103154 A103155 A103156 * A103158 A103159 A103160

KEYWORD

easy,nonn

AUTHOR

Hugo Pfoertner, Feb 12 2005

STATUS

approved