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%I #30 May 28 2023 10:27:10
%S 1,43,505,3067,12559,39733,104959,242845,507781,980407,1775005,
%T 3047815,5006275,7919185,12127795,18057817,26232361,37285795,51978529,
%U 71212723,96048919,127723597,167667655
%N Crystal ball sequence for A_6 lattice.
%C Partial sums of A008387.
%H T. D. Noe, <a href="/A008388/b008388.txt">Table of n, a(n) for n = 0..1000</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/Cor#crystal_ball">Index entries for crystal ball sequences</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 a(n) = 1+7*n*(n+1)*(n^2+n+3)*(11*n^2+11*n+14)/60. - _T. D. Noe_, Apr 29 2007
%F G.f.: (1+36*x+225*x^2+400*x^3+225*x^4+36*x^5+x^6)/(1-x)^7. [_Colin Barker_, Mar 15 2012]
%o (Maxima) A008388[n]:=1+7*n*(n+1)*(n^2+n+3)*(11*n^2+11*n+14)/60$
%o makelist(A008388[n],n,0,30); /* _Martin Ettl_, Oct 26 2012 */
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_ and _J. H. Conway_
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