A350597 -id:A350597 - 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.

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, 17, 16, 17, 18, 19, 20, 21, 20, 21, 20, 21, 22, 23, 24, 25, 26, 29, 28, 29, 28, 29, 30, 31, 32, 33, 32, 33, 32, 31, 34, 35, 36, 37, 38, 37, 40, 41, 42, 43, 44, 45, 44, 45, 46, 47

Offset: 1

David Williams, May 29 2022

nonn

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.

All the above statements apply to A350597.

			                  X                1
  1 2             1 2              0      Thus, 1, 0, 1, 0, 1, 0, 1, 2, ...
  1 3             1 3 X            1
  1 3 5 6         1 3 5 6          0
  1 3 5 7         1 3 5 7 X        1
  1 3 5 7 9 10    1 3 5 7 9 10     0

David Williams, Table of n, a(n) for n = 1..103

Cf. A335105, A350597.

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.

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