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
KEYWORD
nonn,easy
AUTHOR
Natan Arie Consigli, May 28 2016
STATUS
approved