A271998 Volatile sequence: a(n) = A018227(n)-6.

30, 48, 80, 112, 162, 212, 284, 356, 454, 552, 680, 808, 970, 1132, 1332, 1532, 1774, 2016, 2304, 2592, 2930, 3268, 3660, 4052, 4502, 4952, 5464, 5976, 6554, 7132, 7780, 8428, 9150, 9872, 10672, 11472, 12354, 13236, 14204, 15172, 16230, 17288, 18440

Offset: 3

Author

Natan Arie Consigli, Jun 27 2016

Keywords

• nonn
• easy

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).

Programs

Mathematica

LinearRecurrence[{2,1,-4,1,2,-1},{30,48,80,112,162,212},50] (* Harvey P. Dale, Mar 07 2022 *)

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

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)