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A103157 Number of ways to chose 4 distinct points from an (n+1)X(n+1)X(n+1) lattice cube. 4
70, 17550, 635376, 9691375, 88201170, 566685735, 2829877120, 11671285626, 41417124750, 130179173740, 370215608400, 968104633665, 2357084537626, 5396491792125, 11710951848960, 24246290643940, 48151733324310, 92140804597626, 170538695998000, 306294282269955 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

Index to sequences with 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: A229776 A231054 A007100 * A007099 A004109 A002829

Adjacent sequences:  A103154 A103155 A103156 * A103158 A103159 A103160

KEYWORD

easy,nonn

AUTHOR

Hugo Pfoertner, Feb 12 2005

STATUS

approved

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Last modified November 27 17:39 EST 2014. Contains 250249 sequences.