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

1,2

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).

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)

Prog

(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

Crossrefs

Sequence in context: A086711 A039514 A098797 * A317453 A339247 A317678

Adjacent sequences: A271996 A271997 A271998 * A272000 A272001 A272002

Keyword

nonn,easy,changed

Author

Natan Arie Consigli, Jul 02 2016

Status

approved