A157079 a(n) = 32805000*n^2 - 10513800*n + 842401.

23133601, 111034801, 264546001, 483667201, 768398401, 1118739601, 1534690801, 2016252001, 2563423201, 3176204401, 3854595601, 4598596801, 5408208001, 6283429201, 7224260401, 8230701601, 9302752801, 10440414001, 11643685201

Offset

1,1

Comments

The identity (32805000*n^2 - 10513800*n + 842401)^2 - (2025*n^2 - 3401*n + 1428)*(729000*n - 116820)^2 = 1 can be written as a(n)^2 - A156854(n)*A156866(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*(23133601 + 41633998*x + 842401*x^2)/(1-x)^3.

E.g.f.: -842401 + (842401 + 22291200*x + 32805000*x^2)*exp(x). - G. C. Greubel, Jan 27 2022

Mathematica

LinearRecurrence[{3, -3, 1}, {23133601, 111034801, 264546001}, 40]

Prog

(Magma) I:=[23133601, 111034801, 264546001]; [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)=32805000*n^2-10513800*n+842401 \\ Charles R Greathouse IV, Dec 23 2011
(Sage) [16200*n*(2025*n - 649) + 842401 for n in (1..30)] # G. C. Greubel, Jan 27 2022

Crossrefs

Cf. A156854, A156866, A157078, A157080, A157081.

Sequence in context: A235931 A204414 A114666 * A321065 A183736 A105238

Adjacent sequences: A157076 A157077 A157078 * A157080 A157081 A157082

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 22 2009

Status

approved