OFFSET
2,1
COMMENTS
Terms up to 113 are the atomic numbers of the elements of group 13 in the periodic table. Those elements are also called icosagens.
LINKS
G. C. Greubel, Table of n, a(n) for n = 2..1000
Index entries for linear recurrences with constant coefficients, signature (2, 1, -4, 1, 2, -1).
FORMULA
From G. C. Greubel, Jun 23 2016: (Start)
a(n) = n*((n+3)^2 + 2)/6 + (n+2)*(1+(-1)^n)/4 - 6, for n >= 2.
a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).
G.f.: x^2 * (5 + 3*x - 6*x^3 - x^4 + 3*x^5)/( (1-x)^4 * (1+x)^2 ). (End)
MATHEMATICA
Table[n*((n+3)^2 + 2)/6 + (n+2)*(1+(-1)^n)/4 - 6, {n, 2, 10}] (* or *) LinearRecurrence[{2, 1, -4, 1, 2, -1}, {5, 13, 31, 49, 81, 113}, 50] (* G. C. Greubel, Jun 23 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Natan Arie Consigli, Jun 19 2016
STATUS
approved