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Table T(n,k) composed of rows equal to: n * (the characteristic function of the multiples of (n+1)), read by downwards antidiagonals.
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%I #11 Dec 10 2016 02:23:29

%S 1,0,2,1,0,3,0,0,0,4,1,2,0,0,5,0,0,0,0,0,6,1,0,3,0,0,0,7,0,2,0,0,0,0,

%T 0,8,1,0,0,4,0,0,0,0,9,0,0,0,0,0,0,0,0,0,10

%N Table T(n,k) composed of rows equal to: n * (the characteristic function of the multiples of (n+1)), read by downwards antidiagonals.

%C Column k =1 of the table is the integers, from n=1 in row 1.

%C The n-th row of the table is a repeating pattern, starting with the value of n followed by n instances of zero, as created by the characteristic function of the multiples of (n+1).

%C Sums of the antidiagonals produce A065608.

%C Row 1 is A059841, row 2 = 2*A079978, row 3 = 3*A121262, row 4 = 4*A079998, row 5 = 5*A079979, row 6 = 6*A082784, row 7 = 7*|A014025|. - _Boris Putievskiy_, May 08 2013

%F From _Boris Putievskiy_, May 08 2013: (Start)

%F As table T(n,k)= n*(floor((n+k)/(n+1)-floor((n+k-1)/(n+1)).

%F As linear sequence a(n) = A002260(n)*(floor(A003057(n))/(A002260(n)+1)-floor(A002024(n))/(A002260(n)+1)); a(n)=i*(floor((t+2)/(i+1)-floor((t+1)/(i+1)), where i=n-t*(t+1)/2, t=floor((-1+sqrt(8*n-7))/2). (End)

%e 1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0 ...

%e 2,0,0,2,0,0,2,0,0,2,0,0,2,0,0,2,0,0 ...

%e 3,0,0,0,3,0,0,0,3,0,0,0,3,0,0,0,3,0 ...

%e 4,0,0,0,0,4,0,0,0,0,4,0,0,0,0,4,0,0 ...

%e 5,0,0,0,0,0,5,0,0,0,0,0,5,0,0,0,0,0 ...

%e 6,0,0,0,0,0,0,6,0,0,0,0,0,0,6,0,0,0 ...

%e 7,0,0,0,0,0,0,0,7,0,0,0,0,0,0,0,7,0 ...

%e 8,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0 ...

%e 9,0,0,0,0,0,0,0,0,0,9,0,0,0,0,0,0,0 ...

%Y Cf. A065608, A002024, A002260, A003057, A059841, A079978, A121262, A079998, A079979, A082784, A014025.

%K nonn,tabl

%O 1,3

%A _Richard R. Forberg_, May 01 2013