|
| |
|
|
A035601
|
|
Number of points of L1 norm 7 in cubic lattice Z^n.
|
|
1
| |
|
|
0, 2, 28, 198, 952, 3530, 10836, 28814, 68464, 148626, 299660, 568150, 1022760, 1761370, 2919620, 4680990, 7288544, 11058466, 16395516, 23810534, 33940120, 47568618, 65652532, 89347502, 120037968, 159369650, 209284972
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
REFERENCES
| J. Serra-Sagrista, Enumeration of lattice points in l_1 norm, Information Processing Letters, 76, no. 1-2 (2000), 39-44.
|
|
|
LINKS
| 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).
Index to sequences with linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
|
|
|
FORMULA
| a(n)= ( 8*n^6 +4*5*7*n^4 +8*7*7*n^2 +2*5*9 )*n/(5*7*9). - Frank Ellermann (hmdmhdfmhdjmzdtjmzdtzktdkztdjz(AT)gmail.com), Mar 16 2002
|
|
|
MAPLE
| f := proc(d, m) local i; sum( 2^i*binomial(d, i)*binomial(m-1, i-1), i=1..min(d, m)); end; # n=dimension, m=norm
|
|
|
PROG
| (PARI) (8*n^7+140*n^5+392*n^3+90*n)/315 \\ Charles R Greathouse IV, Dec 07 2011
|
|
|
CROSSREFS
| Cf. A035596-A035607.
Sequence in context: A065340 A001798 A123787 * A001759 A019441 A147537
Adjacent sequences: A035598 A035599 A035600 * A035602 A035603 A035604
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
