A271999 Halogen sequence: a(n) = A018227(n)-1.

1, 11, 17, 35, 53, 85, 117, 167, 217, 289, 361, 459, 557, 685, 813, 975, 1137, 1337, 1537, 1779, 2021, 2309, 2597, 2935, 3273, 3665, 4057, 4507, 4957, 5469, 5981, 6559, 7137, 7785, 8433, 9155, 9877, 10677, 11477, 12359, 13241, 14209, 15177, 16235, 17293

Offset: 1

Author

Natan Arie Consigli, Jul 02 2016

Keywords

• nonn
• easy

Comments

Terms from 11 to 117 are the atomic numbers of the elements in group 17 in the periodic table. The elements in this group are also called halogens.

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Programs

Mathematica

LinearRecurrence[{2, 1, -4, 1, 2, -1}, {1, 11, 17, 35, 53, 85, 117, 167}, 50] (* Paolo Xausa, Oct 21 2024 *)

PARI

Vec(x*(1 + 9*x - 6*x^2 - 6*x^3 + 9*x^4 - x^5 - 4*x^6 + 2*x^7) / ((1 - x)^4*(1 + x)^2) + O(x^50)) \\ Colin Barker, Nov 14 2017

Formula

From Colin Barker, Nov 14 2017: (Start)

G.f.: x*(1 + 9*x - 6*x^2 - 6*x^3 + 9*x^4 - x^5 - 4*x^6 + 2*x^7) / ((1 - x)^4*(1 + x)^2).

a(n) = (1/12)*(2*n^3 + 12*n^2 + 28*n - 12) for n>2 and even.

a(n) = (1/12)*(2*n^3 + 12*n^2 + 22*n - 24) for n>2 and 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>8.

(End)