A349723 Atomic number corresponding to the element that is the first of the two middle elements in the n-th row of the periodic table of elements.

1, 6, 14, 27, 45, 70, 102, 143, 193, 254, 326, 411, 509, 622, 750, 895, 1057, 1238, 1438, 1659, 1901, 2166, 2454, 2767, 3105, 3470, 3862, 4283, 4733, 5214, 5726, 6271, 6849, 7462, 8110, 8795, 9517, 10278, 11078, 11919, 12801, 13726, 14694, 15707

Offset

1,2

Comments

Elements corresponding to the initial sequence terms are hydrogen, carbon, silicon, cobalt, rhodium, ytterbium, and nobelium. However, there may not be a physical realization for higher terms.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

Formula

a(n) = A018227(n-1) + A093907(n)/2 for n > 1.

a(n) = (A018227(n) + A018227(n-1))/2 for n > 1.

a(n) = (4*n^3 + 18*n^2 + 32*n + 3*(-1)^n - 27)/24.

G.f.: x*(1 + 3*x - 2*x^2 - x^3 + x^4)/((1 - x)^4*(1 + x)). - Stefano Spezia, Dec 31 2021

Example

For n=1, hydrogen (with atomic number 1) is the first element of two middle elements in the 1st row of periodic table.
For n=2, carbon (with atomic number 6) is the first element of the two middle elements in the 2nd row of periodic table.
In general, the n-th number is the addition of the atomic number of the first lower noble element plus half the number of elements in the current row of the periodic table.

Mathematica

A349723[n_] := (3*((-1)^n - 9) + 2*n*(n*(2*n + 9) + 16))/24;
Array[A349723, 50] (* Paolo Xausa, Jun 30 2026 *)

Crossrefs

Cf. A018227, A093907.

Sequence in context: A107317 A071776 A063590 * A378230 A128806 A139596

Adjacent sequences: A349720 A349721 A349722 * A349724 A349725 A349726

Keyword

nonn,easy,changed

Author

Yigit Oktar, Dec 31 2021

Status

approved