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%I #5 Jan 17 2013 08:31:53
%S 0,0,0,0,1,0,0,0,3,0,0,0,2,7,0,0,0,4,12,15,0,0,0,4,30,50,31,0,0,0,8,
%T 42,160,180,63,0,0,0,4,84,304,750,602,127,0,0,0,12,78,656,1890,3304,
%U 1932,255,0,0,0,8,162,880,4620,10864,14070,6050,511,0,0,0,12,156,1680,8070
%N T(n,k) = Points in n-dimensional lattice of side length k with at least one coordinate = k and GCD of all coordinates = 1.
%F T(n, 0) = 0; T(n, k) = (k+1)^n - k^n - sum T(n, divisors of k)
%e T(3,2) = 12 because of the six permutations of (2,1,0) and three each of (2,1,1) and (2,2,1).
%e 0;
%e 0, 0;
%e 0, 1, 0;
%e 0, 0, 3, 0;
%e 0, 0, 2, 7, 0;
%e 0, 0, 4, 12, 15, 0;
%e 0, 0, 4, 30, 50, 31, 0;
%e 0, 0, 8, 42,160,180, 63, 0;
%e 0, 0, 4, 84,304,750,602,127, 0;
%e 0, 0, 12, 78,656,1890,3304,1932,255, 0;
%t aux[n_, k_] := If[k == 0, 0, (k + 1)^n - k^n - Sum[aux[n, Divisors[k][[i]]], {i, 1, Length[Divisors[k]] - 1}]]
%Y Cf. A090030.
%K nonn,tabl
%O 0,9
%A _Joshua Zucker_, Nov 24 2003
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