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

Offset

0,2

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).

Formula

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

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 *)

Crossrefs

Sequence in context: A250143 A069594 A124338 * A190421 A178387 A068849

Adjacent sequences: A008353 A008354 A008355 * A008357 A008358 A008359

Keyword

nonn,easy

Author

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

Status

approved