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A271994
The chalcogen sequence (a(n) = A018227(n)-2).
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.
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
KEYWORD
nonn,easy
AUTHOR
Natan Arie Consigli, May 28 2016
STATUS
approved