0,2

Number of points in simple cubic lattice at n steps from origin.

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 6-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, 6, 12, 8, 0, 0, 0,...] where (1, 6, 12, 8) = row 3 of the Chebyshev triangle A013609. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 19 2008

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 81.

T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (10).

R. G. Stanton and D. D. Cowan, Note on a "square" functional equation, SIAM Rev., 12 (1970), 277-279.

T. D. Noe, Table of n, a(n) for n=0..1000

Index entries for sequences related to linear recurrences with constant coefficients

J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (Abstract, pdf, ps).

Milan Janjic, Two Enumerative Functions

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Index entries for crystal ball sequences

G.f.: (1+x)^3 /(1-x)^4. a(n) = (2*n+1)*(2*n^2+2*n+3)/3.

First differences of A014820(n). - Alexander Adamchuk (alex(AT)kolmogorov.com), May 23 2006

(1/3)*(2*n+1)*(2*n^2+2*n+3);

A001845:=(z+1)**3/(z-1)**4; [Conjectured (correctly) by S. Plouffe in his 1992 dissertation.]

Sums of 2 consecutive terms give A008412.

(1/12)*t*(2*n^3-3*n^2+n)+2*n-1 for t = 2, 4, 6, ... gives A049480, A005894, A063488, A001845, A063489, A005898, A063490, A057813, A063491, A005902, A063492, A005917, A063493, A063494, A063495, A063496.

Partial sums of A005899.

Cf. A001846, A001847, A001848, etc., A014820, A013609.

Sequence in context: A033814 A118395 A118396 this_sequence A127765 A155305 A155290

Adjacent sequences: A001842 A001843 A001844 this_sequence A001846 A001847 A001848

nonn,easy,nice

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

More terms from Larry Reeves (larryr(AT)acm.org), Jul 17 2000