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

%I A225203 #15 Feb 22 2025 23:59:27
%S A225203 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 A225203 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,
%U A225203 0,0,0,0,0,0,0,0,0,0,12,1,0,0,0,0,6,0,0,0,0,0,0,13
%N A225203 Table T(n,k) composed of rows equal to: n * (the characteristic function of the multiples of (n+1)), read by downwards antidiagonals.
%C A225203 Column k =1 of the table is the integers, from n=1 in row 1.
%C A225203 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 A225203 Sums of the antidiagonals produce A065608.
%C A225203 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 A225203 From _Boris Putievskiy_, May 08 2013: (Start)
%F A225203 As table T(n,k) = n*(floor((n+k)/(n+1))-floor((n+k-1)/(n+1))).
%F A225203 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 A225203 Table begins:
%e A225203   1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0 ...
%e A225203   2,0,0,2,0,0,2,0,0,2,0,0,2,0,0,2,0,0 ...
%e A225203   3,0,0,0,3,0,0,0,3,0,0,0,3,0,0,0,3,0 ...
%e A225203   4,0,0,0,0,4,0,0,0,0,4,0,0,0,0,4,0,0 ...
%e A225203   5,0,0,0,0,0,5,0,0,0,0,0,5,0,0,0,0,0 ...
%e A225203   6,0,0,0,0,0,0,6,0,0,0,0,0,0,6,0,0,0 ...
%e A225203   7,0,0,0,0,0,0,0,7,0,0,0,0,0,0,0,7,0 ...
%e A225203   8,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,0,0 ...
%e A225203   9,0,0,0,0,0,0,0,0,0,9,0,0,0,0,0,0,0 ...
%Y A225203 Cf. A065608, A002024, A002260, A003057, A059841, A079978, A121262, A079998, A079979, A082784, A014025.
%K A225203 nonn,tabl,easy
%O A225203 1,3
%A A225203 _Richard R. Forberg_, May 01 2013
%E A225203 More terms from _Jason Yuen_, Feb 22 2025