%I #21 Apr 29 2020 21:24:53
%S 3,11,29,47,79,111,161,211,283,355,453,551,679,807,969,1131,1331,1531,
%T 1773,2015,2303,2591,2929,3267,3659,4051,4501,4951,5463,5975,6553,
%U 7131,7779,8427,9149,9871,10671,11471,12353,13235,14203,15171,16229,17287,18439
%N Coinage sequence: a(n) = A018227(n)-7.
%C Terms from 29 to 111 are the atomic numbers of the elements of group 11 in the periodic table. The group is also known as the coinage metals since copper (element 29), silver (element 47) and gold (element 79) are in group 11.
%H Colin Barker, <a href="/A272000/b272000.txt">Table of n, a(n) for n = 1..1000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Group_11_element">Group 11 element</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_, Oct 25 2016: (Start)
%F G.f.: x*(3 + 5*x + 4*x^2 - 10*x^3 - 3*x^4 + 5*x^5)/((1 - x)^4*(1 + x)^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) for n>6.
%F a(n) = (n^3 + 9*n^2 + 26*n - 30)/6 for n even.
%F a(n) = (n^3 + 9*n^2 + 29*n - 21)/6 for n odd. (End)
%t LinearRecurrence[{2,1,-4,1,2,-1},{3,11,29,47,79,111},50] (* _Harvey P. Dale_, Nov 26 2018 *)
%o (PARI) Vec(x*(3+5*x+4*x^2-10*x^3-3*x^4+5*x^5)/((1-x)^4*(1+x)^2) + O(x^60)) \\ _Colin Barker_, Oct 25 2016
%Y Other groups: 1(A219527), 2(A168380), 3(A168388), 12(A271998), 13(A271997), 14(A271996), 15(A271995), 16(A271994), 17(A271999), 18(A018227).
%K nonn,easy
%O 1,1
%A _Natan Arie Consigli_, Jul 02 2016