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

2,1

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).

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)

Mathematica

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

Prog

(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

Crossrefs

Cf. A018227.

Sequence in context: A159695 A014001 A291642 * A174792 A063592 A159792

Adjacent sequences: A271992 A271993 A271994 * A271996 A271997 A271998

Keyword

nonn,easy

Author

Natan Arie Consigli, Jun 18 2016

Status

approved