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A343599
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T(n,k) is the coordination number of the (n+1)-dimensional cubic lattice for radius k; triangle read by rows, n>=0, 0<=k<=n.
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4
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1, 1, 4, 1, 6, 18, 1, 8, 32, 88, 1, 10, 50, 170, 450, 1, 12, 72, 292, 912, 2364, 1, 14, 98, 462, 1666, 4942, 12642, 1, 16, 128, 688, 2816, 9424, 27008, 68464, 1, 18, 162, 978, 4482, 16722, 53154, 148626, 374274, 1, 20, 200, 1340, 6800, 28004, 97880, 299660, 822560, 2060980, 1, 22, 242, 1782, 9922, 44726, 170610, 568150, 1690370, 4573910, 11414898
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: (1+y)/(1-x-y-x*y).
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EXAMPLE
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The full array starts
1 2 2 2 2 2 2 2 2
1 4 8 12 16 20 24 28 32
1 6 18 38 66 102 146 198 258
1 8 32 88 192 360 608 952 1408
1 10 50 170 450 1002 1970 3530 5890
1 12 72 292 912 2364 5336 10836 20256
1 14 98 462 1666 4942 12642 28814 59906
1 16 128 688 2816 9424 27008 68464 157184
1 18 162 978 4482 16722 53154 148626 374274
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MAPLE
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local g, x, y ;
g := (1+y)/(1-x-y-x*y) ;
coeftayl(%, x=0, n) ;
coeftayl(%, y=0, k) ;
end proc:
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MATHEMATICA
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T[n_, k_] := Module[{x, y}, SeriesCoefficient[(1 + y)/(1 - x - y - x*y), {x, 0, n}] // SeriesCoefficient[#, {y, 0, k}]&];
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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