A271994 The chalcogen sequence (a(n) = A018227(n)-2).

8, 16, 34, 52, 84, 116, 166, 216, 288, 360, 458, 556, 684, 812, 974, 1136, 1336, 1536, 1778, 2020, 2308, 2596, 2934, 3272, 3664, 4056, 4506, 4956, 5468, 5980, 6558, 7136, 7784, 8432, 9154, 9876, 10676, 11476, 12358, 13240, 14208, 15176, 16234, 17292, 18444

Offset: 2

Author

Natan Arie Consigli, May 28 2016

Keywords

• nonn
• easy

Comments

Terms up to 116 are the atomic numbers of the elements of group 16 in the periodic table. Those elements are also known as chalcogens.

Links

• Colin Barker, Table of n, a(n) for n = 2..1000
• Wikipedia, Chalcogen
• Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Programs

Mathematica

Table[(2 n^3 + 12 n^2 + 25 n + (-1)^n 3 (n + 2) - 30)/12, {n, 2, 43}] (* or *)
Drop[#, 2] &@ CoefficientList[Series[2 x^2 (4 - 3 x^2 + x^4)/((1 - x)^4 (1 + x)^2), {x, 0, 43}], x] (* Michael De Vlieger, May 29 2016 *)
LinearRecurrence[{2,1,-4,1,2,-1},{8,16,34,52,84,116},50] (* Harvey P. Dale, Sep 24 2022 *)

PARI

Vec(2*x^2*(4-3*x^2+x^4)/((1-x)^4*(1+x)^2) + O(x^50)) \\ Colin Barker, May 29 2016

Formula

From Colin Barker, May 29 2016: (Start)

a(n) = 2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6) for n>7.

G.f.: 2*x^2*(4-3*x^2+x^4) / ((1-x)^4*(1+x)^2).

(End)

a(n) = (2*n^3 + 12*n^2 + 25*n + (-1)^n*3*(n + 2) - 30)/12. - Ilya Gutkovskiy, May 29 2016