A157796 a(n) = 27225*n^2 - 12098*n + 1344.

16471, 86048, 210075, 388552, 621479, 908856, 1250683, 1646960, 2097687, 2602864, 3162491, 3776568, 4445095, 5168072, 5945499, 6777376, 7663703, 8604480, 9599707, 10649384, 11753511, 12912088, 14125115, 15392592, 16714519

Offset

1,1

Comments

The identity(1482401250*n^2-658736100*n+73180801)^2-(27225*n^2-12098*n+1344)*(8984250*n-1996170)^2=1 can be written as A157798(n)^2-a(n)*A157797(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

G.f.: x*(16471 + 36635*x + 1344*x^2)/(1 - x)^3.

a(1)=16471, a(2)=86048, a(3)=210075; for n>3, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Jul 02 2011

Mathematica

Table[27225 n^2 - 12098 n + 1344, {n, 25}]  (* Harvey P. Dale, Feb 20 2011 *)
LinearRecurrence[{3, -3, 1}, {16471, 86048, 210075}, 25] (* Harvey P. Dale, Jul 02 2011 *)

Prog

(Magma) I:=[16471, 86048, 210075]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..40]];
(PARI) a(n)=27225*n^2-12098*n+1344;

Crossrefs

Cf. A157797, A157798.

Sequence in context: A283027 A031829 A057680 * A186848 A211841 A234054

Adjacent sequences: A157793 A157794 A157795 * A157797 A157798 A157799

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 07 2009

Extensions

Edited by M. F. Hasler, Oct 08 2014

Status

approved