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 if the offset were 1. - Michael J. Welch (mjw1(AT)ntlworld.com), Apr 01 2004, R. J. Mathar, Jul 18 2009

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

Equals binomial transform of [1, 7, 18, 20, 8, 0, 0, 0,...], where (1, 7, 18, 20, 8) = row 4 of the Chebyshev triangle A081277. Also = row 4 of the array in A142978. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 19 2008

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-1) = n^2*(n^2+2)/3. - Corrected R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 18 2009

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.rs), Apr 03 2002

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

sum(1/((1/3*(n^2+2*n+3))*(n+1)^2),n=0..infinity)=(1/4)*Pi^2-3*sqrt(2)*Pi*coth(Pi*sqrt(2))*(1/8)+3/8=1.17585894941174777047662451219168582851913... [From Stephen Crowley (crow(AT)crowlogic.net), Jul 14 2009]

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)];

a:=n->add(2*n+add(n+add(n, j=1..n-1), j=1..n), j=1..n):seq(a(n)/3, n=1..21); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 27 2008]

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

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

Cf. A081277, A142978.

Sequence in context: A118312 A140867 A114105 this_sequence A070736 A051836 A070051

Adjacent sequences: A014817 A014818 A014819 this_sequence A014821 A014822 A014823

nonn

N. J. A. Sloane (njas(AT)research.att.com).

Formula index corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 18 2009