A103157
Number of ways to choose 4 distinct points from an (n+1) X (n+1) X (n+1) lattice cube.
Original entry on oeis.org
70, 17550, 635376, 9691375, 88201170, 566685735, 2829877120, 11671285626, 41417124750, 130179173740, 370215608400, 968104633665, 2357084537626, 5396491792125, 11710951848960, 24246290643940, 48151733324310, 92140804597626, 170538695998000, 306294282269955
Offset: 1
- 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).
A103659
(1/6) * most frequently occurring volume assumed by triangular pyramids with their 4 vertices chosen from distinct points of an (n+1)X(n+1)X(n+1) lattice cube.
Original entry on oeis.org
1, 2, 2, 4, 4, 12, 12, 12, 12, 12, 24, 24, 24, 24
Offset: 1
a(1)=1 because 2*A103660(1)=56 of the 2*A103656(1)=58 triangular pyramids that can be formed from the vertices of a cube have volume=1/6. The other two pyramids have volume=1/3.
Cf.
A103660 = number of occurrences of the most frequent volume. For more cross-references see
A103657.
A103660
(1/2) * number of occurrences of the most frequent volume given in A103659 assumed by triangular pyramids with their 4 vertices chosen from distinct points of an (n+1)X(n+1)X(n+1) lattice cube.
Original entry on oeis.org
28, 2636, 47175, 433800, 2539628, 11995110, 44602758, 139885368, 379716780, 926937330, 2055408018, 4473284223, 8941638240, 16995482919
Offset: 1
A103661
Smallest value of 6*V not occurring in the list of 4-point object volumes assumed by triangular pyramids with their 4 vertices chosen from distinct points of an (n+1)X(n+1)X(n+1) lattice cube.
Original entry on oeis.org
11, 34, 77, 154, 257, 447, 675, 1003, 1391, 1915, 2381, 3200, 3977
Offset: 2
Showing 1-4 of 4 results.