A187881 - OEIS

%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