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Coordination sequence for 39-dimensional cubic lattice.
2

%I #28 Aug 19 2018 06:12:55

%S 1,78,3042,79118,1544322,24138894,314835170,3525405390,34608828930,

%T 302685166030,2388631358178,17185219312014,113694451659906,

%U 696708049377294,3979111519381986,21295193543579982,107295791104411650

%N Coordination sequence for 39-dimensional cubic lattice.

%H Seiichi Manyama, <a href="/A035734/b035734.txt">Table of n, a(n) for n = 0..10000</a>

%H J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http://neilsloane.com/doc/Me220.pdf">pdf</a>).

%H Joan Serra-Sagrista, <a href="http://dx.doi.org/10.1016/S0020-0190(00)00119-8">Enumeration of lattice points in l_1 norm</a>, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.

%H <a href="/index/Rec#order_39">Index entries for linear recurrences with constant coefficients</a>, 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).

%F O.g.f.: ((1+x)/(1-x))^39. [clarified by _Harvey P. Dale_, Apr 09 2015]

%F n*a(n) = 78*a(n-1) + (n-2)*a(n-2) for n > 1. - _Seiichi Manyama_, Aug 18 2018

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

%Y Cf. A035776, A266213 (row 39).

%K nonn,easy

%O 0,2

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

%E Recomputed by _N. J. A. Sloane_, Nov 25 1998