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A051777 Triangle read by rows, where row (n) = n mod n, n mod (n-1), n mod (n-2), ...n mod 1.

%I A051777 #21 Oct 27 2023 22:00:45
%S A051777 0,0,0,0,1,0,0,1,0,0,0,1,2,1,0,0,1,2,0,0,0,0,1,2,3,1,1,0,0,1,2,3,0,2,
%T A051777 0,0,0,1,2,3,4,1,0,1,0,0,1,2,3,4,0,2,1,0,0,0,1,2,3,4,5,1,3,2,1,0,0,1,
%U A051777 2,3,4,5,0,2,0,0,0,0,0,1,2,3,4,5,6,1,3,1,1,1,0,0,1,2,3,4,5,6,0,2,4,2,2,0,0
%N A051777 Triangle read by rows, where row (n) = n mod n, n mod (n-1), n mod (n-2), ...n mod 1.
%C A051777 Also, rectangular array read by antidiagonals, a(n, k) = k mod n (k >= 0, n >= 1). Cf. A048158, A051127. - _David Wasserman_, Oct 01 2008
%C A051777 Central terms: a(2*n - 1, n) = n - 1. - _Reinhard Zumkeller_, Jan 25 2011
%H A051777 Reinhard Zumkeller, <a href="/A051777/b051777.txt">Rows n=1..150 of triangle, flattened</a>
%e A051777 row (5) = 5 mod 5, 5 mod 4, 5 mod 3, 5 mod 2, 5 mod 1 = 0, 1, 2, 1, 0.
%e A051777 0 ;
%e A051777 0  0 ;
%e A051777 0  1  0 ;
%e A051777 0  1  0  0 ;
%e A051777 0  1  2  1  0;
%e A051777 0  1  2  0  0  0 ;
%e A051777 0  1  2  3  1  1  0 ;
%e A051777 0  1  2  3  0  2  0  0;
%e A051777 0  1  2  3  4  1  0  1  0 ;
%e A051777 0  1  2  3  4  0  2  1  0  0 ;
%e A051777 0  1  2  3  4  5  1  3  2  1  0 ;
%e A051777 0  1  2  3  4  5  0  2  0  0  0  0 ;
%e A051777 0  1  2  3  4  5  6  1  3  1  1  1  0 ;
%t A051777 Flatten[Table[Mod[n,Range[n,1,-1]],{n,20}]] (* _Harvey P. Dale_, Nov 30 2011 *)
%o A051777 (Haskell)
%o A051777 a051777 n k = a051777_row n !! (k-1)
%o A051777 a051777_row n = map (mod n) [n, n-1 .. 1]
%o A051777 a051777_tabl = map a051777_row [1..]
%o A051777 -- _Reinhard Zumkeller_, Jan 25 2011
%Y A051777 Cf. A051778. Row sums give A004125. Number of 0's in row n gives A000005 (tau(n)). Number of 1's in row n+1 gives A032741(n).
%K A051777 easy,nice,nonn,tabl
%O A051777 1,13
%A A051777 _Asher Auel_, Dec 09 1999