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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 * A360312 A332368 A203246 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 February 23 02:18 EST 2024. Contains 370265 sequences. (Running on oeis4.)