A156842 529n^2 - 746n + 263.

46, 887, 2786, 5743, 9758, 14831, 20962, 28151, 36398, 45703, 56066, 67487, 79966, 93503, 108098, 123751, 140462, 158231, 177058, 196943, 217886, 239887, 262946, 287063, 312238, 338471, 365762, 394111, 423518, 453983, 485506, 518087

Offset

1,1

Comments

The identity (279841*n^2-394634*n+139128)^2-(529*n^2-746*n+263)*(12167*n-8579)^2=1 can be written as A156844(n)^2-a(n)*A156845(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*(-46-749*x-263*x^2)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {46, 887, 2786}, 40]
Table[529n^2-746n+263, {n, 40}] (* Harvey P. Dale, Jun 07 2023 *)

Prog

(Magma) I:=[46, 887, 2786]; [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)=529*n^2-746*n+263 \\ Charles R Greathouse IV, Dec 23 2011

Crossrefs

Cf. AA156844, A156845, A156849.

Sequence in context: A066405 A113922 A160067 * A078427 A002138 A205495

Adjacent sequences: A156839 A156840 A156841 * A156843 A156844 A156845

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 17 2009

Extensions

Edited by Charles R Greathouse IV, Jul 25 2010

Status

approved