0,2

a(n) is the number of 4 X 4 pandiagonal magic squares with sum 2n. - Sharon Sela (sharonsela(AT)hotmail.com), May 10 2002

Figurate numbers based on the 4-dimensional regular convex polytope called the 16-cell, hexadecachoron, 4-cross polytope or 4-hyperoctahedron with Schlaefli symbol {3,3,4}. a(n)=(n^2*(n^2+2))/3 starting from the index n=1. - Michael J. Welch (mjw1(AT)ntlworld.com), Apr 01 2004

If X is an n-set and Y_i (i=1,2,3) mutually disjoint 2-subsets of X then a(n-6) is equal to the number of 7-subests of X intersecting each Y_i (i=1,2,3). - Milan R. Janjic (agnus(AT)blic.net), Aug 26 2007

Maya Ahmed, Jesus De Loera and Raymond Hemmecke, Polyhedral cones of magic cubes and squares, in Discrete and Computational Geometry, Springer, Berlin, 2003, pp. 25-41,

T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.

Milan Janjic, Two Enumerative Functions

Hyun Kwang Kim, On Regular Polytope Numbers

Eric Weisstein's World of Mathematics, 16-Cell

Or, a(n) = n^2*(n^2+2)/3.

G.f.: (1+x)^3/(1-x)^5. Recurrence: a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 03 2002

a(n-1) = C(n+3,4) + 3 C(n+2,4) + 3 C(n+1,4) + C(n,4)

al:=proc(s, n) binomial(n+s-1, s); end; be:=proc(d, n) local r; add( (-1)^r*binomial(d-1, r)*2^(d-1-r)*al(d-r, n), r=0..d-1); end; [seq(be(4, n), n=0..100)];

Cf. A005900, A070212, A000332, A000583, A092181, A092182, A092183.

Cf. A069038, A069039, A099193, A099195, A099196, A099197, A099175.

Sequence in context: A022274 A118312 A114105 this_sequence A070736 A051836 A070051

Adjacent sequences: A014817 A014818 A014819 this_sequence A014821 A014822 A014823

nonn

njas