A035737 Coordination sequence for 42-dimensional cubic lattice.

1, 84, 3528, 98812, 2076816, 34949796, 490681688, 5913144396, 62456027424, 587522034932, 4985149915368, 38549117382300, 273998113272240, 1803067831236420, 11053262513080440, 63460928860322028, 342841481215636032

Offset

0,2

Comments

First differs from A035806 at a(21). a(21)=721321863363711058916, whereas A035806(21)=721321867761757570020. - Nathaniel Johnston, Jun 26 2011

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..500 from Nathaniel Johnston)

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

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).

Index entries for coordination sequences

Formula

G.f.: ((1+x)/(1-x))^42.

n*a(n) = 84*a(n-1) + (n-2)*a(n-2) for n > 1. - Seiichi Manyama, Aug 27 2018

Maple

t:=taylor(((1+x)/(1-x))^42, x, 30): seq(coeff(t, x, n), n=0..21); # Nathaniel Johnston, Jun 26 2011

Mathematica

CoefficientList[Series[((1+x)/(1-x))^42, {x, 0, 20}], x] (* Harvey P. Dale, Aug 03 2012 *)

Prog

(PARI) Vec((((1+x)/(1-x))^42) + O(x^17)) \\ Felix Fröhlich, Aug 27 2018

Crossrefs

Sequence in context: A026809 A114253 A017800 * A035806 A017747 A223959

Adjacent sequences: A035734 A035735 A035736 * A035738 A035739 A035740

Keyword

nonn,easy

Author

Joan Serra-Sagrista (jserra(AT)ccd.uab.es)

Extensions

Recomputed by N. J. A. Sloane, Nov 25 1998

Status

approved