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A008378
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Coordination sequence for D_10 lattice.
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2
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1, 180, 6440, 94620, 802640, 4687108, 20924280, 76392940, 238753440, 659632980, 1649142216, 3796582460, 8156356080, 16522765220, 31822575640, 58659933324, 104054451520, 178420035060, 296839277160, 480696051420, 759737228432, 1174643272260, 1780196817080
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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 (10,-45,120,-210,252,-210,120,-45,10,-1).
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FORMULA
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G.f.: (x^10 +170*x^9 +4685*x^8 +38200*x^7 +124850*x^6 +183356*x^5 +124850*x^4 +38200*x^3 +4685*x^2 +170*x +1) / (x -1)^10. [Colin Barker, Nov 19 2012]
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MAPLE
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1352/945*n^9+1328/63*n^7+3416/45*n^5+13136/189*n^3+1268/105*n;
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MATHEMATICA
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CoefficientList[Series[(x^10 + 170 x^9 + 4685 x^8 + 38200 x^7 + 124850 x^6 + 183356 x^5 + 124850 x^4 + 38200 x^3 + 4685 x^2 + 170 x + 1)/(x - 1)^10, {x, 0, 50}], x] (* Vincenzo Librandi, Oct 15 2013 *)
LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {1, 180, 6440, 94620, 802640, 4687108, 20924280, 76392940, 238753440, 659632980, 1649142216}, 40] (* Harvey P. Dale, Jun 22 2017 *)
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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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EXTENSIONS
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STATUS
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approved
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