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%I #12 Jan 11 2020 15:57:47
%S 5,13,31,49,81,113,163,213,285,357,455,553,681,809,971,1133,1333,1533,
%T 1775,2017,2305,2593,2931,3269,3661,4053,4503,4953,5465,5977,6555,
%U 7133,7781,8429,9151,9873,10673,11473,12355,13237,14205,15173,16231,17289,18441
%N The icosagen sequence : a(n) = A018227(n)-5, for n >= 2.
%C Terms up to 113 are the atomic numbers of the elements of group 13 in the periodic table. Those elements are also called icosagens.
%H G. C. Greubel, <a href="/A271997/b271997.txt">Table of n, a(n) for n = 2..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 _G. C. Greubel_, Jun 23 2016: (Start)
%F a(n) = n*((n+3)^2 + 2)/6 + (n+2)*(1+(-1)^n)/4 - 6, for n >= 2.
%F a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).
%F G.f.: x^2 * (5 + 3*x - 6*x^3 - x^4 + 3*x^5)/( (1-x)^4 * (1+x)^2 ). (End)
%t Table[n*((n+3)^2 + 2)/6 + (n+2)*(1+(-1)^n)/4 - 6, {n,2,10}] (* or *) LinearRecurrence[{2,1,-4,1,2,-1},{5, 13, 31, 49, 81, 113},50] (* _G. C. Greubel_, Jun 23 2016 *)
%K nonn,easy
%O 2,1
%A _Natan Arie Consigli_, Jun 19 2016
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