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A035477
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Coordination sequence for lattice D*_16 (with edges defined by l_1 norm = 1).
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1
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1, 32, 512, 5472, 44032, 285088, 1549824, 7288544, 30382080, 114509600, 396241408, 1273082976, 3829072896, 10848180384, 29093973504, 74178420192, 180482027520, 420523089440, 941348409856, 2030565262176, 4232440732672, 8546273961888, 16756632155648
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OFFSET
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0,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (16, -120, 560, -1820, 4368, -8008, 11440, -12870, 11440, -8008, 4368, -1820, 560, -120, 16, -1).
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FORMULA
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a(m) = Sum_{k=0..n} (2^k*binomial(n, k)*binomial(m-1, k-1)) + 2^n*binomial((n+2*m)/2-1, n-1), with n=16.
G.f.: (1 +16*x +120*x^2 +560*x^3 +1820*x^4 +4368*x^5 +8008*x^6 +11440*x^7 +78406*x^8 +11440*x^9 +8008*x^10 +4368*x^11 +1820*x^12 +560*x^13 +120*x^14 +16*x^15 +x^16) / (1 -x)^16. - Colin Barker, Dec 23 2015
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MATHEMATICA
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Table[SeriesCoefficient[(1 + 16 x + 120 x^2 + 560 x^3 + 1820 x^4 + 4368 x^5 + 8008 x^6 + 11440 x^7 + 78406 x^8 + 11440 x^9 + 8008 x^10 + 4368 x^11 + 1820 x^12 + 560 x^13 + 120 x^14 + 16 x^15 + x^16)/(1 - x)^16, {x, 0, n}], {n, 0, 22}] (* Michael De Vlieger, Dec 23 2015 *)
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PROG
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(PARI) Vec((1 +16*x +120*x^2 +560*x^3 +1820*x^4 +4368*x^5 +8008*x^6 +11440*x^7 +78406*x^8 +11440*x^9 +8008*x^10 +4368*x^11 +1820*x^12 +560*x^13 +120*x^14 +16*x^15 +x^16) / (1 -x)^16 + O(x^40)) \\ Colin Barker, Dec 23 2015
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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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STATUS
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approved
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