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 A022151 Coordination sequence for root lattice B_9. 4
 1, 162, 5154, 67266, 507906, 2653346, 10666146, 35310402, 100746498, 255708578, 590675490, 1262903490, 2531446530, 4804547490, 8702041250, 15135668034, 25410452994, 41350565538, 65453329442, 101075312322, 152654680578, 225974263458, 328470027426, 469589919554 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES R. Bacher, P. de la Harpe and B. Venkov, Series de croissance et series d'Ehrhart associees aux reseaux de racines, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 M. Baake and U. Grimm, Coordination sequences for root lattices and related graphs, arXiv:cond-mat/9706122, Zeit. f. Kristallographie, 212 (1997), 253-256. Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1). FORMULA a(0)=1; for n>0, a(n) = ( 2012*n^8 - 3952*n^7 + 27160*n^6 - 35392*n^5 + 81508*n^4 - 57568*n^3 + 45560*n^2 - 8928*n + 630 ) / 315. - Ralf Stephan, Apr 28 2004 G.f.: -(x^9 +825*x^8 +11124*x^7 +49380*x^6 +91118*x^5 +74574*x^4 +26628*x^3 +3732*x^2 +153*x +1)/(x -1)^9. - Colin Barker, Nov 18 2012 MATHEMATICA CoefficientList[Series[-(x^9 + 825 x^8 + 11124 x^7 + 49380 x^6 + 91118 x^5 + 74574 x^4 + 26628 x^3 + 3732 x^2 + 153 x + 1)/(x - 1)^9, {x, 0, 30}], x] (* Vincenzo Librandi, Oct 17 2013 *) Join[{1}, LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {162, 5154, 67266, 507906, 2653346, 10666146, 35310402, 100746498, 255708578}, 30]] (* Harvey P. Dale, Mar 23 2015 *) PROG (MAGMA) [1] cat [(2012*n^8-3952*n^7+27160*n^6-35392*n^5+81508*n^4-57568*n^3+45560*n^2 -8928*n+630)/315: n in [1..30]]; // Vincenzo Librandi, Oct 17 2013 CROSSREFS Sequence in context: A128803 A035746 A285046 * A279917 A291131 A209965 Adjacent sequences:  A022148 A022149 A022150 * A022152 A022153 A022154 KEYWORD nonn,easy AUTHOR mbaake(AT)sunelc3.tphys.physik.uni-tuebingen.de (Michael Baake) STATUS approved

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Last modified June 4 07:23 EDT 2020. Contains 334822 sequences. (Running on oeis4.)