A008386 Crystal ball sequence for A_5 lattice.
1, 31, 271, 1281, 4251, 11253, 25493, 51563, 95693, 166003, 272755, 428605, 648855, 951705, 1358505, 1894007, 2586617, 3468647, 4576567, 5951257, 7638259, 9688029, 12156189, 15103779, 18597509
Offset: 0
Links
- T. D. Noe, Table of n, a(n) for n = 0..1000
- J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
- Index entries for crystal ball sequences
- Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
Programs
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Mathematica
LinearRecurrence[{6,-15,20,-15,6,-1},{1,31,271,1281,4251,11253},30] (* Harvey P. Dale, Apr 08 2018 *)
Formula
a(n) = (2*n+1)*(63*n^4+126*n^3+217*n^2+154*n+60)/60. - T. D. Noe, Apr 29 2007
G.f.: (1+x)*(1+24*x+76*x^2+24*x^3+x^4)/(1-x)^6. - Colin Barker, Mar 16 2012
Comments