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A008387
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Coordination sequence for A_6 lattice.
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3
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1, 42, 462, 2562, 9492, 27174, 65226, 137886, 264936, 472626, 794598, 1272810, 1958460, 2912910, 4208610, 5930022, 8174544, 11053434, 14692734, 19234194, 24836196, 31674678, 39944058, 49858158, 61651128, 75578370, 91917462, 110969082
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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).
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FORMULA
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a(n) = S(n,6) = 7*n*(11*n^4 + 35*n^2 + 14)/10, with S(n,m) = Sum_{k=0..m} binomial(m,k)^2 * binomial(n-k+m-1, m-1), for n > 0, and a(0) = 1.
G.f.: (1+36*x+225*x^2+400*x^3+225*x^4+36*x^5+x^6)/(1-x)^6 = 1 + 42*x*(1+5*x+10*x^2+5*x^3+x^4)/(1-x)^6. - Colin Barker, Sep 26 2012
E.g.f.: 1 + (1/10)*x*(420 + 1890*x + 2170*x^2 + 770*x^3 + 77*x^4)*exp(x). - G. C. Greubel, May 26 2023
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MAPLE
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1, seq(7*n*(11*n^4+35*n^2+14)/10, n=1..40);
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MATHEMATICA
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LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 42, 462, 2562, 9492, 27174, 65226}, 30] (* Jean-François Alcover, Jan 07 2019 *)
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PROG
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(Magma) [n eq 0 select 1 else 7*n*(11*n^4+35*n^2+14)/10: n in [0..50]]; // G. C. Greubel, May 26 2023
(SageMath) [7*n*(11*n^4 +35*n^2 +14)/10 +int(n==0) for n in range(51)] # G. C. Greubel, May 26 2023
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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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