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A261046 Irregular triangle read by rows: the first column consists of the odd numbers repeated but without the first 1. Row n (n>=0) contains floor(n/2)=1 terms. Every row contains successive odd numbers.

%I A261046 #32 Nov 20 2015 13:00:05
%S A261046 1,3,3,5,5,7,5,7,9,7,9,11,7,9,11,13,9,11,13,15,9,11,13,15,17,11,13,15,
%T A261046 17,19,11,13,15,17,19,21,13,15,17,19,21,23,13,15,17,19,21,23,25,15,17,
%U A261046 19,21,23,25,27,13,15,17,19,21,23,25,27
%N A261046 Irregular triangle read by rows: the first column consists of the odd numbers repeated but without the first 1. Row n (n>=0) contains floor(n/2)=1 terms. Every row contains successive odd numbers.
%C A261046 A131507(n), not in the same order.
%C A261046 a(n) multiplied by the triangle (extended A249947(n+1)) = (A167268(n+1))/2 is
%C A261046    1,                 1,               1,
%C A261046    3,                 1,               3,
%C A261046    3, 5,              3, 1,            9, 5,
%C A261046    5, 7,          *   3, 1,       =   15, 7,
%C A261046    5, 7,  9,          5, 3, 1,        25, 21, 9
%C A261046    7, 9, 11,          5, 3, 1,        35, 27, 11,
%C A261046    etc.               etc.            etc.
%C A261046 The latter triangle is the odd numbers of A094728(n+1) which is
%C A261046    1,
%C A261046    4,  3,
%C A261046    9,  8,  5,
%C A261046   16, 15, 12,  7,
%C A261046   25, 24, 21, 16, 9,
%C A261046   etc.
%C A261046 Without the first column, the triangle is A120070(n+2). This gives a link between the frequencies of the spectral lines of the H-atom and the Janet periodic table of the elements.
%e A261046 Triangle begins:
%e A261046 1,
%e A261046 3,
%e A261046 3,  5,
%e A261046 5,  7,
%e A261046 5,  7,  9,
%e A261046 7,  9, 11,
%e A261046 7,  9, 11, 13,
%e A261046 9, 11, 13, 15,
%e A261046 9, 11, 13, 15, 17,
%e A261046 ....
%Y A261046 Cf. A094728, A120070, A131507, A167268, A249947.
%K A261046 nonn,tabf
%O A261046 0,2
%A A261046 _Paul Curtz_, Nov 19 2015