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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.
0
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.
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.
CROSSREFS
Sequence in context: A107317 A071776 A063590 * A378230 A128806 A139596
KEYWORD
nonn,easy
AUTHOR
Yigit Oktar, Dec 31 2021
STATUS
approved