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A125202
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a(n) = 4*n^2 - 6*n + 1.
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15
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-1, 5, 19, 41, 71, 109, 155, 209, 271, 341, 419, 505, 599, 701, 811, 929, 1055, 1189, 1331, 1481, 1639, 1805, 1979, 2161, 2351, 2549, 2755, 2969, 3191, 3421, 3659, 3905, 4159, 4421, 4691, 4969, 5255, 5549, 5851, 6161, 6479, 6805, 7139, 7481, 7831, 8189, 8555, 8929, 9311, 9701, 10099, 10505, 10919, 11341
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = A125199(n,n-1) for n>1.
A003415(a(n)) = A017089(n-1).
From Arkadiusz Wesolowski, Dec 25 2011: (Start)
a(1) = -1, a(n) = a(n-1) + 8*n - 10.
a(n) = 2*a(n-1) - a(n-2) + 8 with a(1) = -1 and a(2) = 5.
G.f.: (1 - 4*x + 11*x^2)/(1 - x)^3. (End)
a(n) = A002943(n-1) - 1. - Arkadiusz Wesolowski, Feb 15 2012
a(n) = A028387(2n-3), with A028387(-1) = -1. - Vincenzo Librandi, Oct 10 2013
E.g.f.: exp(x)*(1 - 2*x + 4*x^2). - Stefano Spezia, Oct 10 2022
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MATHEMATICA
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f[a_]:=4*a^2-6*a+1; lst={}; Do[AppendTo[lst, f[n]], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 14 2009 *)
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PROG
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(Magma) [4*n^2 - 6*n + 1: n in [1..60]]; // Vincenzo Librandi, Jul 11 2011
(PARI) a(n)=4*n^2-6*n+1 \\ Charles R Greathouse IV, Sep 28 2015
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CROSSREFS
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Cf. A125199.
Cf. A003415, A017089.
Cf. A002939, A016789, A017041, A017485, A028387.
Cf. A002943, A028387.
Sequence in context: A146600 A262997 A031379 * A024841 A155737 A100572
Adjacent sequences: A125199 A125200 A125201 * A125203 A125204 A125205
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KEYWORD
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sign,easy
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AUTHOR
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Reinhard Zumkeller, Nov 24 2006
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STATUS
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approved
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