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%I #11 Apr 25 2024 09:33:23
%S 1,11,17,35,53,85,117,167,217,289,361,459,557,685,813,975,1137,1337,
%T 1537,1779,2021,2309,2597,2935,3273,3665,4057,4507,4957,5469,5981,
%U 6559,7137,7785,8433,9155,9877,10677,11477,12359,13241,14209,15177,16235,17293
%N Halogen sequence: a(n) = A018227(n)-1.
%C Terms from 11 to 117 are the atomic numbers of the elements in group 17 in the periodic table. The elements in this group are also called halogens.
%H Colin Barker, <a href="/A271999/b271999.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F From _Colin Barker_, Nov 14 2017: (Start)
%F G.f.: x*(1 + 9*x - 6*x^2 - 6*x^3 + 9*x^4 - x^5 - 4*x^6 + 2*x^7) / ((1 - x)^4*(1 + x)^2).
%F a(n) = (1/12)*(2*n^3 + 12*n^2 + 28*n - 12) for n>2 and even.
%F a(n) = (1/12)*(2*n^3 + 12*n^2 + 22*n - 24) for n>2 and odd.
%F 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>8.
%F (End)
%o (PARI) Vec(x*(1 + 9*x - 6*x^2 - 6*x^3 + 9*x^4 - x^5 - 4*x^6 + 2*x^7) / ((1 - x)^4*(1 + x)^2) + O(x^50)) \\ _Colin Barker_, Nov 14 2017
%K nonn,easy
%O 1,2
%A _Natan Arie Consigli_, Jul 02 2016
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