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 A008377 Crystal ball sequence for D_9 lattice. 4
 1, 145, 4339, 55171, 416773, 2218645, 9195511, 31608967, 94016137, 249258777, 601883259, 1345167627, 2817026445, 5581287453, 10542186111, 19101404943, 33368594193, 56438048673, 92746082819, 148525641875, 232376811797, 355974143909, 534934092551, 789868374935 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified May 26 23:01 EDT 2024. Contains 372847 sequences. (Running on oeis4.)