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%I #16 Jun 13 2015 00:51:38
%S 70,17550,635376,9691375,88201170,566685735,2829877120,11671285626,
%T 41417124750,130179173740,370215608400,968104633665,2357084537626,
%U 5396491792125,11710951848960,24246290643940,48151733324310,92140804597626,170538695998000,306294282269955
%N Number of ways to choose 4 distinct points from an (n+1) X (n+1) X (n+1) lattice cube.
%H T. D. Noe, <a href="/A103157/b103157.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F a(n) = binomial((n+1)^3, 4).
%F 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
%Y 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.
%K easy,nonn
%O 1,1
%A _Hugo Pfoertner_, Feb 12 2005
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