cp's OEIS Frontend

A354445 Number of polynomials per row where the minimum number of rows and polynomials per row necessary to transform A335105 into a triangular array are present.

%I A354445 #24 Dec 31 2023 14:09:55
%S A354445 1,0,1,0,1,0,1,2,3,4,5,4,5,4,5,6,7,8,9,8,9,8,9,10,11,12,13,14,15,16,
%T A354445 17,16,17,18,19,20,21,20,21,20,21,22,23,24,25,26,29,28,29,28,29,30,31,
%U A354445 32,33,32,33,32,31,34,35,36,37,38,37,40,41,42,43,44,45,44,45,46,47
%N A354445 Number of polynomials per row where the minimum number of rows and polynomials per row necessary to transform A335105 into a triangular array are present.
%C A354445 This array treats A335105, an irregular triangle, as a subset of a symmetrical one. It is only necessary to add one row in order to transform A335105 into a triangular array. Rows two, four and six, which correspond to Hydrogen, Lithium and Boron in A335105, are the only rows composed entirely of numerical terms; for these rows the terminal number divided by two and then squared equals the sum of terms left of the right edge. Polynomials within a row may change places with numerical terms within the same row without changing the number of polynomials per row. Given that the summands of A335105 (shell and number of shell's electrons) are necessarily added in multiples of two, the parity of this sequence is alternating.
%C A354445 All the above statements apply to A350597.
%H A354445 David Williams, <a href="/A354445/b354445.txt">Table of n, a(n) for n = 1..103</a>
%e A354445                   X                1
%e A354445   1 2             1 2              0      Thus, 1, 0, 1, 0, 1, 0, 1, 2, ...
%e A354445   1 3             1 3 X            1
%e A354445   1 3 5 6         1 3 5 6          0
%e A354445   1 3 5 7         1 3 5 7 X        1
%e A354445   1 3 5 7 9 10    1 3 5 7 9 10     0
%Y A354445 Cf. A335105, A350597.
%K A354445 nonn
%O A354445 1,8
%A A354445 _David Williams_, May 29 2022