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%I #25 Dec 13 2022 10:07:49
%S 1,0,2,0,2,3,0,0,3,4,0,0,3,4,5,0,0,0,4,5,6,0,0,0,4,5,6,7,0,0,0,0,5,6,
%T 7,8,0,0,0,0,5,6,7,8,9,0,0,0,0,0,6,7,8,9,10,0,0,0,0,0,6,7,8,9,10,11
%N Triangle read by rows: the n-th column consists of n n's followed by 0's.
%C Row sums = A001318: (1, 2, 5, 7, 12,...)
%C The triangle is a variant of Janet's periodic table:
%C .......1
%C .......2
%C .....2,3
%C .....3,4
%C ...3,4,5
%C ...4,5,6
%C .4,5,6,7
%C .5,6,7,8
%C ...
%H Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations (of) Integer Sequences And Pairing Functions</a>, arXiv:1212.2732 [math.CO], 2012.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Electron_configuration">Electron configuration</a>
%F As an infinite lower triangular matrix, A * B, where A = A101688 and B = an infinite lower triangular matrix with (1, 2, 3,...) as the main diagonal and the rest zeros.
%F From _Boris Putievskiy_, Jan 09 2013: (Start)
%F a(n) = A101688(n-1)*A002260(n). [Corrected by _Georg Fischer_, Dec 13 2022]
%F a(n) = floor((2*A002260(n)+1)/(A003056(n)+3))*A002260(n).
%F a(n) = floor((2*n-t*(t+1)+1)/(t+3))*(n-t*(t+1)/2), where t = floor((-1+sqrt(8*n-7))/2). (End)
%e First few rows of the triangle:
%e 1
%e 0, 2
%e 0, 2, 3
%e 0, 0, 3, 4
%e 0, 0, 3, 4, 5
%e 0, 0, 0, 4, 5, 6
%e 0, 0, 0, 4, 5, 6, 7
%e ...
%Y Cf. A001318, A101688.
%K nonn,easy,tabl
%O 1,3
%A _Gary W. Adamson_, Mar 14 2011
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