A157078 a(n) = 32805000*n^2 - 55096200*n + 23133601.

842401, 44161201, 153090001, 327628801, 567777601, 873536401, 1244905201, 1681884001, 2184472801, 2752671601, 3386480401, 4085899201, 4850928001, 5681566801, 6577815601, 7539674401, 8567143201, 9660222001, 10818910801, 12043209601

Offset

1,1

Comments

The identity(32805000*n^2 - 55096200*n + 23133601)^2 - (2025*n^2 - 649*n + 52)*(729000*n - 612180)^2 = 1 can be written as a(n)^2 - A156853(n)*A156865(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*(842401 + 41633998*x + 23133601*x^2)/(1-x)^3.

E.g.f.: -23133601 + (23133601 - 22291200*x + 32805000*x^2)*exp(x). - G. C. Greubel, Jan 27 2022

Mathematica

LinearRecurrence[{3, -3, 1}, {842401, 44161201, 153090001}, 40]

Prog

(Magma) I:=[842401, 44161201, 153090001]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..30]];
(PARI) a(n)=32805000*n^2-55096200*n+23133601 \\ Charles R Greathouse IV, Dec 23 2011
(Sage) [16200*n*(2025*n - 3401) + 23133601 for n in (1..25)] # G. C. Greubel, Jan 27 2022

Crossrefs

Cf. A156853, A156865, A157079, A157080, A157081.

Sequence in context: A263038 A043623 A185520 * A160548 A259014 A251017

Adjacent sequences: A157075 A157076 A157077 * A157079 A157080 A157081

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 22 2009

Status

approved