A157378 a(n) = 43046721*n^2 - 50729652*n + 14945957.

7263026, 85673537, 250177490, 500774885, 837465722, 1260250001, 1769127722, 2364098885, 3045163490, 3812321537, 4665573026, 5604917957, 6630356330, 7741888145, 8939513402, 10223232101, 11593044242, 13048949825, 14590948850, 16219041317

Offset

1,1

Comments

The identity (43046721*n^2 - 50729652*n + 14945959)^2 - (6561*n^2 - 7732*n + 2278)*(531441*n - 313146)^2 = 1 can be written as a(n)^2 - A157376(n)*A157377(n)^2 = 1.

Links

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

Vincenzo Librandi, X^2-AY^2=1

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*(7263026 + 63884459*x + 14945957*x^2)/(1-x)^3.

E.g.f.: (6561*x*(6561*x - 1171) + 14945957)*exp(x) - 14945957. - G. C. Greubel, Feb 04 2018

Mathematica

LinearRecurrence[{3, -3, 1}, {7263026, 85673537, 250177490}, 40]
Table[43046721*n^2 - 50729652*n + 14945957, {n, 1, 30}] (* G. C. Greubel, Feb 04 2018 *)

Prog

(Magma) I:=[7263026, 85673537, 250177490]; [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) =  43046721*n^2 - 50729652*n + 14945957.

Crossrefs

Cf. A157376, A157377.

Sequence in context: A181680 A253469 A325606 * A251356 A116236 A116259

Adjacent sequences: A157375 A157376 A157377 * A157379 A157380 A157381

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 28 2009, Mar 08 2009

Status

approved