A035734 Coordination sequence for 39-dimensional cubic lattice.

1, 78, 3042, 79118, 1544322, 24138894, 314835170, 3525405390, 34608828930, 302685166030, 2388631358178, 17185219312014, 113694451659906, 696708049377294, 3979111519381986, 21295193543579982, 107295791104411650

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 (39, -741, 9139, -82251, 575757, -3262623, 15380937, -61523748, 211915132, -635745396, 1676056044, -3910797436, 8122425444, -15084504396, 25140840660, -37711260990, 51021117810, -62359143990, 68923264410, -68923264410, 62359143990, -51021117810, 37711260990, -25140840660, 15084504396, -8122425444, 3910797436, -1676056044, 635745396, -211915132, 61523748, -15380937, 3262623, -575757, 82251, -9139, 741, -39, 1).

Crossrefs

Cf. A035776, A266213 (row 39).

Programs

Mathematica

CoefficientList[Series[((1+n)/(1-n))^39,{n,0,20}],n] (* Harvey P. Dale, Apr 09 2015 *)

Formula

O.g.f.: ((1+x)/(1-x))^39. [clarified by Harvey P. Dale, Apr 09 2015]

n*a(n) = 78*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