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

3,1

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

Sequence in context: A004223 A230558 A272949 * A365965 A307130 A228097

Adjacent sequences: A271995 A271996 A271997 * A271999 A272000 A272001

Keyword

nonn,easy

Author

Natan Arie Consigli, Jun 27 2016

Status

approved