login
A225203
Table T(n,k) composed of rows equal to: n * (the characteristic function of the multiples of (n+1)), read by downwards antidiagonals.
0
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, 0, 8, 1, 0, 0, 4, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10
OFFSET
1,3
COMMENTS
Column k =1 of the table is the integers, from n=1 in row 1.
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).
Sums of the antidiagonals produce A065608.
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
FORMULA
From Boris Putievskiy, May 08 2013: (Start)
As table T(n,k)= n*(floor((n+k)/(n+1)-floor((n+k-1)/(n+1)).
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)
EXAMPLE
1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0 ...
2,0,0,2,0,0,2,0,0,2,0,0,2,0,0,2,0,0 ...
3,0,0,0,3,0,0,0,3,0,0,0,3,0,0,0,3,0 ...
4,0,0,0,0,4,0,0,0,0,4,0,0,0,0,4,0,0 ...
5,0,0,0,0,0,5,0,0,0,0,0,5,0,0,0,0,0 ...
6,0,0,0,0,0,0,6,0,0,0,0,0,0,6,0,0,0 ...
7,0,0,0,0,0,0,0,7,0,0,0,0,0,0,0,7,0 ...
8,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0 ...
9,0,0,0,0,0,0,0,0,0,9,0,0,0,0,0,0,0 ...
KEYWORD
nonn,tabl
AUTHOR
Richard R. Forberg, May 01 2013
STATUS
approved