A035708 Coordination sequence for 13-dimensional cubic lattice.

1, 26, 338, 2938, 19266, 101946, 454610, 1761370, 6065410, 18892250, 53972178, 143027898, 354870594, 830764794, 1847023698, 3921503898, 7988589570, 15677993370, 29746958930, 54734043130, 97926519106, 170763634106, 290835675858

Offset: 0

Author

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

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• 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 (13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1).

Crossrefs

Cf. A035750, A266213 (row 13).

Programs

Mathematica

CoefficientList[Series[((1+x)/(1-x))^13,{x,0,30}],x] (* or *) LinearRecurrence[ {13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1},{1,26,338,2938,19266,101946,454610,1761370,6065410,18892250,53972178,143027898,354870594,830764794},30] (* Harvey P. Dale, Nov 07 2017 *)

Formula

G.f.: ((1+x)/(1-x))^13.

n*a(n) = 26*a(n-1) + (n-2)*a(n-2) for n > 1. - Seiichi Manyama, Aug 18 2018

Extensions

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