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A272000
Coinage sequence: a(n) = A018227(n)-7.
1
3, 11, 29, 47, 79, 111, 161, 211, 283, 355, 453, 551, 679, 807, 969, 1131, 1331, 1531, 1773, 2015, 2303, 2591, 2929, 3267, 3659, 4051, 4501, 4951, 5463, 5975, 6553, 7131, 7779, 8427, 9149, 9871, 10671, 11471, 12353, 13235, 14203, 15171, 16229, 17287, 18439
OFFSET
1,1
COMMENTS
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.
FORMULA
From Colin Barker, Oct 25 2016: (Start)
G.f.: x*(3 + 5*x + 4*x^2 - 10*x^3 - 3*x^4 + 5*x^5)/((1 - x)^4*(1 + x)^2).
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.
a(n) = (n^3 + 9*n^2 + 26*n - 30)/6 for n even.
a(n) = (n^3 + 9*n^2 + 29*n - 21)/6 for n odd. (End)
MATHEMATICA
LinearRecurrence[{2, 1, -4, 1, 2, -1}, {3, 11, 29, 47, 79, 111}, 50] (* Harvey P. Dale, Nov 26 2018 *)
PROG
(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
CROSSREFS
Other groups: 1(A219527), 2(A168380), 3(A168388), 12(A271998), 13(A271997), 14(A271996), 15(A271995), 16(A271994), 17(A271999), 18(A018227).
Sequence in context: A018743 A077279 A269891 * A196190 A111227 A111693
KEYWORD
nonn,easy
AUTHOR
Natan Arie Consigli, Jul 02 2016
STATUS
approved