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A271996
The crystallogen sequence (a(n) = A018227(n)-4).
2
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.
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
Sequence in context: A350107 A024932 A273365 * A199705 A225972 A332724
KEYWORD
nonn,easy
AUTHOR
Natan Arie Consigli, Jun 18 2016
STATUS
approved