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

2,1

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).

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A043891 A331930 A072578 * A058516 A366511 A217672

Adjacent sequences: A271991 A271992 A271993 * A271995 A271996 A271997

Keyword

nonn,easy

Author

Natan Arie Consigli, May 28 2016

Status

approved