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A271997 The icosagen sequence : a(n) = A018227(n)-5, for n >= 2. 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 (list; graph; refs; listen; history; text; internal format)
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 * A332368 A203246 A106985

Adjacent sequences:  A271994 A271995 A271996 * A271998 A271999 A272000

KEYWORD

nonn,easy

AUTHOR

Natan Arie Consigli, Jun 19 2016

STATUS

approved

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Last modified September 16 18:26 EDT 2021. Contains 347473 sequences. (Running on oeis4.)