A051777 - OEIS

%I #21 Oct 27 2023 22:00:45

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

%C 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 Central terms: a(2*n - 1, n) = n - 1. - _Reinhard Zumkeller_, Jan 25 2011

%H Reinhard Zumkeller, <a href="/A051777/b051777.txt">Rows n=1..150 of triangle, flattened</a>

%e row (5) = 5 mod 5, 5 mod 4, 5 mod 3, 5 mod 2, 5 mod 1 = 0, 1, 2, 1, 0.

%e 0 ;

%e 0  0 ;

%e 0  1  0 ;

%e 0  1  0  0 ;

%e 0  1  2  1  0;

%e 0  1  2  0  0  0 ;

%e 0  1  2  3  1  1  0 ;

%e 0  1  2  3  0  2  0  0;

%e 0  1  2  3  4  1  0  1  0 ;

%e 0  1  2  3  4  0  2  1  0  0 ;

%e 0  1  2  3  4  5  1  3  2  1  0 ;

%e 0  1  2  3  4  5  0  2  0  0  0  0 ;

%e 0  1  2  3  4  5  6  1  3  1  1  1  0 ;

%t Flatten[Table[Mod[n,Range[n,1,-1]],{n,20}]] (* _Harvey P. Dale_, Nov 30 2011 *)

%o (Haskell)

%o a051777 n k = a051777_row n !! (k-1)

%o a051777_row n = map (mod n) [n, n-1 .. 1]

%o a051777_tabl = map a051777_row [1..]

%o -- _Reinhard Zumkeller_, Jan 25 2011

%Y 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 easy,nice,nonn,tabl

%O 1,13

%A _Asher Auel_, Dec 09 1999