A271995 The Pnictogen sequence: a(n) = A018227(n)-3.

7, 15, 33, 51, 83, 115, 165, 215, 287, 359, 457, 555, 683, 811, 973, 1135, 1335, 1535, 1777, 2019, 2307, 2595, 2933, 3271, 3663, 4055, 4505, 4955, 5467, 5979, 6557, 7135, 7783, 8431, 9153, 9875, 10675, 11475, 12357, 13239, 14207, 15175, 16233, 17291, 18443

Offset: 2

Author

Natan Arie Consigli, Jun 18 2016

Keywords

• nonn
• easy

Comments

Terms up to 115 are the atomic numbers of the elements of group 15 in the periodic table. Those elements are also known as pnictogens.

Links

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

Crossrefs

Cf. A018227.

Programs

Mathematica

LinearRecurrence[{2,1,-4,1,2,-1},{7,15,33,51,83,115},50] (* Harvey P. Dale, Oct 29 2023 *)

PARI

Vec(x^2*(7+x-4*x^2-2*x^3+x^4+x^5)/((1-x)^4*(1+x)^2) + O(x^100)) \\ Colin Barker, Jun 19 2016, corrected Jun 26 2016

Formula

From Colin Barker, Jun 19 2016, corrected Jun 26 2016: (Start)

a(n) = (6*(-7+(-1)^n)+(25+3*(-1)^n)*n+12*n^2+2*n^3)/12.

a(n) = (n^3+6*n^2+14*n-18)/6 for n even.

a(n) = (n^3+6*n^2+11*n-24)/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.: x^2*(7+x-4*x^2-2*x^3+x^4+x^5) / ((1-x)^4*(1+x)^2).

(End)