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A156855
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a(n) = 2025*n^2 - n.
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4
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2024, 8098, 18222, 32396, 50620, 72894, 99218, 129592, 164016, 202490, 245014, 291588, 342212, 396886, 455610, 518384, 585208, 656082, 731006, 809980, 893004, 980078, 1071202, 1166376, 1265600, 1368874, 1476198, 1587572, 1702996, 1822470
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OFFSET
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1,1
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COMMENTS
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The identity (32805000*n^2 - 16200*n+1)^2 - (2025*n^2 - n)*(729000*n - 180)^2 = 1 can be written as A157080(n)^2 - a(n)*A156867(n)^2 = 1.
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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) = 3*a(n-1) -3*a(n-2) +a(n-3).
G.f.: x*(2024+2026*x)/(1-x)^3.
E.g.f.: x*(2024 + 2025*x)*exp(x). - G. C. Greubel, Jan 28 2022
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MATHEMATICA
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Table[n (2025*n - 1), {n, 40}] (* Wesley Ivan Hurt, Oct 10 2021 *)
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PROG
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(MAGMA) I:=[2024, 8098, 18222]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n)=2025*n^2-n \\ Charles R Greathouse IV, Dec 23 2011
(Sage) [n*(2025*n -1) for n in (1..40)] # G. C. Greubel, Jan 28 2022
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CROSSREFS
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Cf. A156856, A156867, A157080.
Sequence in context: A257766 A126821 A333057 * A306870 A126172 A183999
Adjacent sequences: A156852 A156853 A156854 * A156856 A156857 A156858
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Feb 17 2009; corrected Feb 20 2009
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STATUS
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approved
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