A225203 - OEIS

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, 1, 2, 3, 0, 5, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 1, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 13

(list; table; graph; refs; listen; history; text; internal format)

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..91.

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

Table begins:

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