OFFSET
3,1
COMMENTS
Terms up to 112 are the atomic numbers of the elements of group 12 in the periodic table. The group is also known as the volatile metals since almost all elements with that property fall in to group 12.
LINKS
Colin Barker, Table of n, a(n) for n = 3..1000
Wikipedia, Group 12 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.: 2*x^3*(15 - 6*x - 23*x^2 + 12*x^3 + 10*x^4 - 6*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>8.
a(n) = (n^3 + 9*n^2 + 26*n - 24)/6 for n even.
a(n) = (n^3 + 9*n^2 + 29*n - 15)/6 for n odd. (End)
MATHEMATICA
LinearRecurrence[{2, 1, -4, 1, 2, -1}, {30, 48, 80, 112, 162, 212}, 50] (* Harvey P. Dale, Mar 07 2022 *)
PROG
(PARI) Vec(2*x^3*(15-6*x-23*x^2+12*x^3+10*x^4-6*x^5)/((1-x)^4*(1+x)^2) + O(x^60)) \\ Colin Barker, Oct 25 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Natan Arie Consigli, Jun 27 2016
STATUS
approved