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A035473
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Coordination sequence for lattice D*_8 (with edges defined by l_1 norm = 1).
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1
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1, 16, 128, 688, 3072, 11472, 36224, 99184, 241664, 535440, 1097344, 2107952, 3834880, 6661200, 11119488, 17932016, 28057600, 42745616, 63597696, 92637616, 132389888, 185967568, 257169792, 350589552, 471732224, 627145360, 824560256, 1073045808, 1383175168
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OFFSET
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0,2
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LINKS
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FORMULA
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a(m) = sum(2^k*binomial(n, k)*binomial(m-1, k-1), k=0..n)+2^n*binomial((n+2*m)/2-1, n-1), where n=8, a(0)=1.
G.f.: (x^8+8*x^7+28*x^6+56*x^5+326*x^4+56*x^3+28*x^2+8*x+1) / (x-1)^8. [Colin Barker, Nov 19 2012]
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MATHEMATICA
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CoefficientList[Series[(x^8 + 8 x^7 + 28 x^6 + 56 x^5 + 326 x^4 + 56 x^3 + 28 x^2 + 8 x + 1)/(x - 1)^8, {x, 0, 50}], x] (* Vincenzo Librandi, Oct 21 2013 *)
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PROG
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(Magma) n:=8; [1] cat [&+[2^k*Binomial(n, k)*Binomial(m-1, k-1): k in [0..n]]+2^n*Binomial((n+2*m) div 2-1, n-1): m in [1..30]]; // Bruno Berselli, 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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EXTENSIONS
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STATUS
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approved
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