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

Offset: 1

Author

Richard R. Forberg, May 01 2013

Keywords

• nonn
• tabl
• easy

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

Examples

			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

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

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)

Extensions

More terms from Jason Yuen, Feb 22 2025