A272000 Coinage sequence: a(n) = A018227(n)-7.

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

Author

Natan Arie Consigli, Jul 02 2016

Keywords

• nonn
• easy

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.

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Wikipedia, Group 11 element.
• Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Crossrefs

Other groups: 1(A219527), 2(A168380), 3(A168388), 12(A271998), 13(A271997), 14(A271996), 15(A271995), 16(A271994), 17(A271999), 18(A018227).

Programs

Mathematica

LinearRecurrence[{2,1,-4,1,2,-1},{3,11,29,47,79,111},50] (* Harvey P. Dale, Nov 26 2018 *)

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

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)