A008358 Crystal ball sequence for D_6 lattice.

1, 61, 853, 5577, 23673, 76389, 204205, 476113, 1000753, 1939405, 3520837, 6058009, 9966633, 15785589, 24199197, 36061345, 52421473, 74552413, 103980085, 142515049, 192285913, 255774597, 335853453

Offset: 0

Author

N. J. A. Sloane and J. H. Conway

Keywords

• nonn
• easy

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Index entries for crystal ball sequences
• 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 linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Programs

Maple

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

Mathematica

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 *)

Formula

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