A225203 Table T(n,k) composed of rows equal to: n * (the characteristic function of the multiples of (n+1)), read by downwards antidiagonals.

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

Links

Table of n, a(n) for n=1..55.

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 ...

Crossrefs

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

Sequence in context: A266832 A373570 A307772 * A136255 A194812 A305320

Adjacent sequences: A225200 A225201 A225202 * A225204 A225205 A225206

Keyword

nonn,tabl

Author

Richard R. Forberg, May 01 2013

Status

approved