A271997 The icosagen sequence : a(n) = A018227(n)-5, for n >= 2.

5, 13, 31, 49, 81, 113, 163, 213, 285, 357, 455, 553, 681, 809, 971, 1133, 1333, 1533, 1775, 2017, 2305, 2593, 2931, 3269, 3661, 4053, 4503, 4953, 5465, 5977, 6555, 7133, 7781, 8429, 9151, 9873, 10673, 11473, 12355, 13237, 14205, 15173, 16231, 17289, 18441

Offset: 2

Author

Natan Arie Consigli, Jun 19 2016

Keywords

• nonn
• easy

Comments

Terms up to 113 are the atomic numbers of the elements of group 13 in the periodic table. Those elements are also called icosagens.

Links

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

Programs

Mathematica

Table[n*((n+3)^2 + 2)/6 + (n+2)*(1+(-1)^n)/4 - 6, {n,2,10}] (* or *) LinearRecurrence[{2,1,-4,1,2,-1},{5, 13, 31, 49, 81, 113},50] (* G. C. Greubel, Jun 23 2016 *)

Formula

From G. C. Greubel, Jun 23 2016: (Start)

a(n) = n*((n+3)^2 + 2)/6 + (n+2)*(1+(-1)^n)/4 - 6, for n >= 2.

a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).

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