A157080 a(n) = 32805000*n^2 - 16200*n + 1.

32788801, 131187601, 295196401, 524815201, 820044001, 1180882801, 1607331601, 2099390401, 2657059201, 3280338001, 3969226801, 4723725601, 5543834401, 6429553201, 7380882001, 8397820801, 9480369601

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 a(n)^2 - A156855(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*(32788801 + 32821198*x + x^2)/(1-x)^3.

E.g.f.: -1 + (1 + 32788800*x + 32805000*x^2)*exp(x). - G. C. Greubel, Jan 27 2022

Mathematica

LinearRecurrence[{3, -3, 1}, {32788801, 131187601, 295196401}, 40]

Prog

(Magma) I:=[32788801, 131187601, 295196401]; [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^2-16200*n+1 \\ Charles R Greathouse IV, Dec 23 2011
(Sage) [16200*n*(2025*n -1) + 1 for n in (1..30)] # G. C. Greubel, Jan 27 2022

Crossrefs

Cf. A156855, A156867, A157078, A157079, A157081.

Sequence in context: A209912 A290264 A206043 * A157081 A015354 A256356

Adjacent sequences: A157077 A157078 A157079 * A157081 A157082 A157083

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 22 2009

Status

approved