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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
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
KEYWORD
nonn,easy
AUTHOR
Natan Arie Consigli, Jun 19 2016
STATUS
approved

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Last modified February 23 02:18 EST 2024. Contains 370265 sequences. (Running on oeis4.)