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A239287 Triangle T(n,k), 0 <= k <= n, read by rows: T(n,k) = floor(n/2) - min(k,n-k).

%I A239287 #22 May 23 2025 23:46:14
%S A239287 0,0,0,1,0,1,1,0,0,1,2,1,0,1,2,2,1,0,0,1,2,3,2,1,0,1,2,3,3,2,1,0,0,1,
%T A239287 2,3,4,3,2,1,0,1,2,3,4,4,3,2,1,0,0,1,2,3,4,5,4,3,2,1,0,1,2,3,4,5,5,4,
%U A239287 3,2,1,0,0,1,2,3,4,5,6,5,4,3,2,1,0,1,2
%N A239287 Triangle T(n,k), 0 <= k <= n, read by rows: T(n,k) = floor(n/2) - min(k,n-k).
%C A239287 Row sums are A110660(n).
%H A239287 G. C. Greubel, <a href="/A239287/b239287.txt">Rows, n=0..100 of triangle, flattened</a>
%F A239287 T(n,k) = floor(n/2) - min(k,n-k).
%e A239287 Triangle begins:
%e A239287 0;
%e A239287 0, 0;
%e A239287 1, 0, 1;
%e A239287 1, 0, 0, 1;
%e A239287 2, 1, 0, 1, 2;
%e A239287 2, 1, 0, 0, 1, 2;
%e A239287 3, 2, 1, 0, 1, 2, 3;
%e A239287 3, 2, 1, 0, 0, 1, 2, 3;
%e A239287 4, 3, 2, 1, 0, 1, 2, 3, 4;
%e A239287 4, 3, 2, 1, 0, 0, 1, 2, 3, 4;
%e A239287 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5;
%e A239287 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5;
%e A239287 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6;
%e A239287 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6;
%e A239287 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7;
%e A239287 7, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 7;
%e A239287 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8;
%e A239287 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8;
%e A239287 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9;
%e A239287 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9;
%t A239287 Column[Table[Floor[n/2] - Min[k, n - k], {n,0, 19}, {k, 0, n}]] (* _Indranil Ghosh_, Mar 15 2017 *)
%o A239287 (PARI) tabl(nn) = {for(n=0, nn, for(k=0, n, print1(floor(n/2) - min(k, n - k),", ");); print(););};
%o A239287 tabl(19); \\ _Indranil Ghosh_, Mar 15 2017
%o A239287 (Python)
%o A239287 i=0
%o A239287 for n in range(0,20):
%o A239287     for k in range(0, n+1):
%o A239287         print(str(i)+" "+str((n//2) - min(k, n - k)))
%o A239287         i+=1 # _Indranil Ghosh_, Mar 15 2017
%o A239287 (Magma) [[Floor(n/2) - Min(k,n-k): k in [0..n]]: n in [0..10]]; // _G. C. Greubel_, May 26 2018
%Y A239287 Cf. A004526.
%K A239287 nonn,tabl
%O A239287 0,11
%A A239287 _Philippe Deléham_, Mar 14 2014