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

Author

Yigit Oktar, Dec 31 2021

Keywords

• nonn
• easy

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A018227, A093907.

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