

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. 4point 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



