A271996 The crystallogen sequence (a(n) = A018227(n)-4).

6, 14, 32, 50, 82, 114, 164, 214, 286, 358, 456, 554, 682, 810, 972, 1134, 1334, 1534, 1776, 2018, 2306, 2594, 2932, 3270, 3662, 4054, 4504, 4954, 5466, 5978, 6556, 7134, 7782, 8430, 9152, 9874, 10674, 11474, 12356, 13238, 14206, 15174, 16232, 17290, 18442

Offset

2,1

Comments

Terms up to 114 are the atomic numbers of the elements of group 14 in the periodic table. Those elements are also called crystallogens.

Links

Colin Barker, Table of n, a(n) for n = 2..1000

Wikipedia, Carbon group.

Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Formula

From Colin Barker, Jun 19 2016: (Start)

a(n) = (6*(-9 + (-1)^n) + (25 + 3*(-1)^n)*n + 12*n^2 + 2*n^3)/12.

a(n) = (n^3 + 6*n^2 + 14*n - 24)/6 for n even.

a(n) = (n^3 + 6*n^2 + 11*n - 30)/6 for n odd.

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>7.

G.f.: 2*x^2*(3 + x - x^2 - 2*x^3 + x^5) / ((1-x)^4*(1+x)^2).

(End)

Mathematica

Table[(6*(-9+(-1)^n)+(25+3*(-1)^n)*n+12*n^2+2*n^3)/12, {n, 2, 10}] (* or *) LinearRecurrence[{2, 1, -4, 1, 2, -1}, {6, 14, 32, 50, 82, 114}, 50] (* G. C. Greubel, Jun 23 2016 *)

Prog

(PARI) Vec(2*x^2*(3+x-x^2-2*x^3+x^5)/((1-x)^4*(1+x)^2) + O(x^100)) \\ Colin Barker, Jun 19 2016

Crossrefs

Cf. A173592, A018227.

Sequence in context: A350107 A024932 A273365 * A199705 A225972 A332724

Adjacent sequences: A271993 A271994 A271995 * A271997 A271998 A271999

Keyword

nonn,easy

Author

Natan Arie Consigli, Jun 18 2016

Status

approved