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

1,8

Comments

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.

Links

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

Example

                  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

Crossrefs

Cf. A335105, A350597.

Sequence in context: A017850 A305901 A291520 * A317646 A305748 A302981

Adjacent sequences: A354442 A354443 A354444 * A354446 A354447 A354448

Keyword

nonn

Author

David Williams, May 29 2022

Status

approved