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A035806
Coordination sequence for lattice D*_42 (with edges defined by l_1 norm = 1).
2
1, 84, 3528, 98812, 2076816, 34949796, 490681688, 5913144396, 62456027424, 587522034932, 4985149915368, 38549117382300, 273998113272240, 1803067831236420, 11053262513080440, 63460928860322028, 342841481215636032, 1750035197354015124
OFFSET
0,2
COMMENTS
Starts to differ from A035737 at a(21). - R. J. Mathar, Oct 24 2008
LINKS
Joan Serra-Sagrista, Enumeration of lattice points in l_1 norm, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.
Index entries for linear recurrences with constant coefficients, signature (42, -861, 11480, -111930, 850668, -5245786, 26978328, -118030185, 445891810, -1471442973, 4280561376, -11058116888, 25518731280, -52860229080, 98672427616, -166509721602, 254661927156, -353697121050, 446775310800, -513791607420, 538257874440, -513791607420, 446775310800, -353697121050, 254661927156, -166509721602, 98672427616, -52860229080, 25518731280, -11058116888, 4280561376, -1471442973, 445891810, -118030185, 26978328, -5245786, 850668, -111930, 11480, -861, 42, -1).
FORMULA
a(n) = (Sum_{k=0..m} 2^k*binomial(m, k)*binomial(n-1, k-1)) + 2^m*binomial((m+2*n)/2-1, m-1), with m=42.
MAPLE
seq(add(2^k*binomial(42, k)*binomial(n-1, k-1), k=0..42) + 2^42*binomial((42+2*n)/2-1, 41), n=0..21); # Nathaniel Johnston, Jun 26 2011
CROSSREFS
Sequence in context: A114253 A017800 A035737 * A017747 A223959 A143402
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, J. Serra-Sagrista (jserra(AT)ccd.uab.es)
STATUS
approved