A008356 Crystal ball sequence for D_5 lattice.

1, 41, 411, 2051, 6981, 18733, 42783, 86983, 161993, 281713, 463715, 729675, 1105805, 1623285, 2318695, 3234447, 4419217, 5928377, 7824427, 10177427, 13065429, 16574909, 20801199, 25848919, 31832409, 38876161, 47115251, 56695771, 67775261, 80523141, 95121143

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 (6,-15,20,-15,6,-1).

Programs

Maple

18/5*n^5+9*n^4+38/3*n^3+10*n^2+71/15*n+1;

Mathematica

CoefficientList[Series[(1+x)*(1+34*x+146*x^2+34*x^3+x^4)/(1-x)^6,{x,0,30}],x] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{1,41,411,2051,6981,18733},30] (* Harvey P. Dale, Sep 03 2016 *)

Formula

G.f.: (1+x)*(1+34*x+146*x^2+34*x^3+x^4)/(1-x)^6. - Colin Barker, Mar 16 2012