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 A008362 Crystal ball sequence for D_8 lattice. 4
 1, 113, 2705, 28129, 177697, 807505, 2908337, 8818625, 23429185, 56070193, 123302609, 252868001, 489082465, 899992081, 1586639089, 2694819713, 4429746305, 7074058225, 11009657617, 16743877985 (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 (9, -36, 84, -126, 126, -84, 36, -9, 1). FORMULA a(n) = 248/315*n^8+992/315*n^7+32/3*n^6+944/45*n^5+144/5*n^4+1184/45*n^3+992/63*n^2+584/105*n+1 (see MAPLE line). G.f.: (1+104*x+1724*x^2+7768*x^3+12550*x^4+7768*x^5+1724*x^6+104*x^7+x^8)/(1-x)^9. [Colin Barker, Mar 16 2012] MAPLE 248/315*n^8+992/315*n^7+32/3*n^6+944/45*n^5+144/5*n^4+1184/45*n^3+992/63*n^2+584/105*n+1; MATHEMATICA CoefficientList[Series[(1+104*x+1724*x^2+ 7768* x^3+12550*x^4+7768*x^5+1724*x^6+104*x^7+x^8)/(1-x)^9, {x, 0, 1003}], x] (* Vincenzo Librandi, Apr 16 2012 *) PROG (Magma) [248/315*n^8+992/315*n^7+32/3*n^6+944/45*n^5+ 144/5*n^4+1184/45*n^3+992/63*n^2+584/105*n+1: n in [0..30]]; // Vincenzo Librandi, Apr 16 2012 CROSSREFS Sequence in context: A079098 A187519 A301529 * A262074 A200854 A012031 Adjacent sequences: A008359 A008360 A008361 * A008363 A008364 A008365 KEYWORD nonn,easy,changed AUTHOR N. J. A. Sloane and J. H. Conway STATUS approved

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Last modified June 2 06:55 EDT 2023. Contains 363081 sequences. (Running on oeis4.)