%I #23 Jul 23 2019 07:59:54

%S 1,61,853,5577,23673,76389,204205,476113,1000753,1939405,3520837,

%T 6058009,9966633,15785589,24199197,36061345,52421473,74552413,

%U 103980085,142515049,192285913,255774597,335853453

%N Crystal ball sequence for D_6 lattice.

%H T. D. Noe, <a href="/A008358/b008358.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Cor#crystal_ball">Index entries for crystal ball sequences</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 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F G.f.: (1+54*x+447*x^2+852*x^3+447*x^4+54*x^5+x^6)/(1-x)^7. - _Colin Barker_, Mar 16 2012

%p 116/45*n^6+116/15*n^5+136/9*n^4+52/3*n^3+554/45*n^2+74/15*n+1;

%t CoefficientList[Series[(1+54x+447x^2+852x^3+447x^4+54x^5+x^6)/(1-x)^7,{x,0,30}],x] (* _Harvey P. Dale_, Jan 23 2019 *)

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_ and _J. H. Conway_