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
KEYWORD
nonn,easy
AUTHOR
Natan Arie Consigli, Jul 02 2016
STATUS
approved