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A035839
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Coordination sequence for A_13 lattice.
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2
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1, 182, 8372, 176722, 2206932, 18827718, 120353324, 614266354, 2619716554, 9654482474, 31534801116, 93093230958, 252208679268, 634756203018, 1498750896708, 3346707628446, 7114703302434, 14479567043214, 28342922553764, 53573492643034, 98118326104708
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OFFSET
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0,2
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LINKS
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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 linear recurrences with constant coefficients, signature (13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1).
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FORMULA
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Sum_{d=1..13} C(14, d)*C(m/2-1, d-1)*C(13-d+m/2, m/2), where norm m is always even.
G.f.: -(x+1)*(x^12 + 168*x^11 + 5916*x^10 + 75880*x^9 + 435345*x^8 + 1221024*x^7 + 1723632*x^6 + 1221024*x^5 + 435345*x^4 + 75880*x^3 + 5916*x^2 + 168*x + 1) / (x-1)^13. [Colin Barker, Nov 19 2012]
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MATHEMATICA
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CoefficientList[Series[-(x + 1) (x^12 + 168 x^11 + 5916 x^10 + 75880 x^9 + 435345 x^8 + 1221024 x^7 + 1723632 x^6 + 1221024 x^5 + 435345 x^4 + 75880 x^3 + 5916 x^2 + 168 x + 1)/(x - 1)^13, {x, 0, 30}], x] (* Vincenzo Librandi, Oct 21 2013 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Joan Serra-Sagrista (jserra(AT)ccd.uab.es)
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EXTENSIONS
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STATUS
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approved
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