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

2,1

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).

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)

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 *)

Crossrefs

Sequence in context: A086522 A234372 A102725 * A360312 A332368 A203246

Adjacent sequences: A271994 A271995 A271996 * A271998 A271999 A272000

Keyword

nonn,easy

Author

Natan Arie Consigli, Jun 19 2016

Status

approved