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

1,1

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.

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).

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

Adjacent sequences: A271997 A271998 A271999 * A272001 A272002 A272003

Keyword

nonn,easy

Author

Natan Arie Consigli, Jul 02 2016

Status

approved