A008377 Crystal ball sequence for D_9 lattice.

1, 145, 4339, 55171, 416773, 2218645, 9195511, 31608967, 94016137, 249258777, 601883259, 1345167627, 2817026445, 5581287453, 10542186111, 19101404943, 33368594193, 56438048673, 92746082819, 148525641875, 232376811797, 355974143909, 534934092551, 789868374935

Offset

0,2

Links

Vincenzo Librandi, 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 (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

a(n-1) = 1006/2835*n^9-503/315*n^8+6404/945*n^7-244/15*n^6+3946/135*n^5-542/15*n^4+87068/2835*n^3-5356/315*n^2+1867/315*n-1.

G.f.: (x+1) * (x^8 +134*x^7 +2800*x^6 +15386*x^5 +27742*x^4 +15386*x^3 +2800*x^2 +134*x +1) / (x-1)^10. [Colin Barker, May 28 2012]

Maple

1006/2835*n^9-503/315*n^8+6404/945*n^7-244/15*n^6+3946/135*n^5-542/15*n^4+87068/2835*n^3-5356/315*n^2+1867/315*n-1;

Mathematica

CoefficientList[Series[(x + 1) (x^8 + 134 x^7 + 2800 x^6 + 15386 x^5 + 27742 x^4 + 15386 x^3 + 2800 x^2 + 134 x + 1)/(x - 1)^10, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 15 2013 *)
LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {1, 145, 4339, 55171, 416773, 2218645, 9195511, 31608967, 94016137, 249258777}, 30] (* Harvey P. Dale, May 11 2024 *)

Crossrefs

Sequence in context: A234116 A232151 A264284 * A076464 A018232 A192842

Adjacent sequences: A008374 A008375 A008376 * A008378 A008379 A008380

Keyword

nonn,easy

Author

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

Extensions

More terms from Vincenzo Librandi, Oct 15 2013

Status

approved