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A035840
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Coordination sequence for A_14 lattice.
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2
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1, 210, 11130, 269570, 3838590, 37060506, 265953170, 1511679210, 7125357540, 28818500830, 102644594262, 328512273390, 959882556570, 2593322651430, 6545498596110, 15564971674518, 35117045235720, 75613799423610, 156153427053890, 310601807143530
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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 (14, -91, 364, -1001, 2002, -3003, 3432, -3003, 2002, -1001, 364, -91, 14, -1).
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FORMULA
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Sum_{d=1..14} C(15, d)*C(m/2-1, d-1)*C(14-d+m/2, m/2), where norm m is always even.
G.f.: (x^14 + 196*x^13 + 8281*x^12 + 132496*x^11 + 1002001*x^10 + 4008004*x^9 + 9018009*x^8 + 11778624*x^7 + 9018009*x^6 + 4008004*x^5 + 1002001*x^4 + 132496*x^3 + 8281*x^2 + 196*x + 1) / (x-1)^14. [Colin Barker, Nov 19 2012]
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MATHEMATICA
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CoefficientList[Series[(x^14 + 196 x^13 + 8281 x^12 + 132496 x^11 + 1002001 x^10 + 4008004 x^9 + 9018009 x^8 + 11778624 x^7 + 9018009 x^6 + 4008004 x^5 + 1002001 x^4 + 132496 x^3 + 8281 x^2 + 196 x + 1)/(x - 1)^14, {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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