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A156855 a(n) = 2025*n^2 - n. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

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

MATHEMATICA

Table[n (2025*n - 1), {n, 40}] (* Wesley Ivan Hurt, Oct 10 2021 *)

PROG

(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

CROSSREFS

Cf. A156856, A156867, A157080.

Sequence in context: A257766 A126821 A333057 * A306870 A126172 A183999

Adjacent sequences:  A156852 A156853 A156854 * A156856 A156857 A156858

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Feb 17 2009; corrected Feb 20 2009

STATUS

approved

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Last modified August 10 16:24 EDT 2022. Contains 356039 sequences. (Running on oeis4.)