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 A008349 Crystal ball sequence for E_8 lattice. (Formerly M5419) 3
 1, 241, 9361, 131041, 996001, 5109841, 20015281, 64495681, 179375041, 444798001, 1006201681, 2111519521, 4162485601, 7783236241, 13909734001, 23903867521, 39696408961, 63963339121, 100340378641, 153680892001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, 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). M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908. Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1). FORMULA G.f.: (1 + 232*x + 7228*x^2 + 55384*x^3 + 133510*x^4 + 107224*x^5 + 24508*x^6 + 232*x^7 + x^8)/(1 - x)^9. a(0)=1, a(1)=241, a(2)=9361, a(3)=131041, a(4)=996001, a(5)=5109841, a(6)=20015281, a(7)=64495681, a(8)=179375041, a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9). - Harvey P. Dale, Jun 12 2012 MAPLE 57/7*n^8+108/7*n^7+30*n^6+72*n^5+39*n^4+36*n^3+300/7*n^2-24/7*n+1; MATHEMATICA CoefficientList[Series[(1+232x+7228x^2+107224x^5+133510x^4+ 55384x^3+ 24508x^6+ 232x^7+ x^8)/(1-x)^9, {x, 0, 30}], x] (* or *) LinearRecurrence[ {9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 241, 9361, 131041, 996001, 5109841, 20015281, 64495681, 179375041}, 30] (* Harvey P. Dale, Jun 12 2012 *) PROG (Python) A008349_list, m = [], [328320, -1071360, 1347840, -812160, 233280, -25920, 240, 0, 1] for _ in range(10**2):     A008349_list.append(m[-1])     for i in range(8):         m[i+1] += m[i] # Chai Wah Wu, Dec 15 2015 (MAGMA) [57/7*n^8 + 108/7*n^7 + 30*n^6 + 72*n^5 + 39*n^4 + 36*n^3 + 300/7*n^2 - 24/7*n + 1: n in [0..40]]; // Vincenzo Librandi, Dec 16 2015 (PARI) a(n)=(57*n^8 + 108*n^7 + 210*n^6 + 504*n^5 + 273*n^4 + 252*n^3 + 300*n^2 - 24*n + 7)/7 \\ Charles R Greathouse IV, Feb 10 2017 CROSSREFS Sequence in context: A165375 A183887 A007205 * A094732 A119728 A133327 Adjacent sequences:  A008346 A008347 A008348 * A008350 A008351 A008352 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS The values given by O'Keeffe are incorrect. STATUS approved

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Last modified January 22 09:37 EST 2019. Contains 319363 sequences. (Running on oeis4.)