%I #84 Jan 01 2022 00:21:28
%S 1,6,14,27,45,70,102,143,193,254,326,411,509,622,750,895,1057,1238,
%T 1438,1659,1901,2166,2454,2767,3105,3470,3862,4283,4733,5214,5726,
%U 6271,6849,7462,8110,8795,9517,10278,11078,11919,12801,13726,14694,15707
%N 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.
%C 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.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).
%F a(n) = A018227(n-1) + A093907(n)/2 for n > 1.
%F a(n) = (A018227(n) + A018227(n-1))/2 for n > 1.
%F a(n) = (4*n^3 + 18*n^2 + 32*n + 3*(-1)^n - 27)/24.
%F G.f.: x*(1 + 3*x - 2*x^2 - x^3 + x^4)/((1 - x)^4*(1 + x)). - _Stefano Spezia_, Dec 31 2021
%e For n=1, hydrogen (with atomic number 1) is the first element of two middle elements in the 1st row of periodic table.
%e For n=2, carbon (with atomic number 6) is the first element of the two middle elements in the 2nd row of periodic table.
%e 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.
%Y Cf. A018227, A093907.
%K nonn,easy
%O 1,2
%A _Yigit Oktar_, Dec 31 2021