A111216 a(n) = 31*a(n-1)-a(n-2).

1, 30, 929, 28769, 890910, 27589441, 854381761, 26458245150, 819351217889, 25373429509409, 785756963573790, 24333092441278081, 753540108716046721, 23335410277756170270, 722644178501725231649, 22378634123275726010849, 693015013643045781104670

Offset

0,2

Comments

Take 31 numbers consisting of 29 ones together with any two successive terms from this sequence. This set has the property that the sum of their squares is 31 times their product. (Guy)

Positive values of x (or y) satisfying x^2 - 31xy + y^2 + 29 = 0. - Colin Barker, Feb 24 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (31,-1).

Formula

G.f.: (1-x)/(1-31*x+x^2). [Philippe Deléham, Nov 18 2008]

a(n) = A200442(n) - A200442(n-1). - R. J. Mathar, Feb 13 2016

Mathematica

CoefficientList[Series[(1 - x)/(1 - 31 x + x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 26 2014 *)

Prog

(PARI) Vec((1-x)/(1-31*x+x^2) + O(x^100)) \\ Colin Barker, Feb 24 2014
(Magma) I:=[1, 30]; [n le 2 select I[n] else 31*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Feb 26 2014

Crossrefs

Cf. A049685.

Cf. similar sequences listed in A238379.

Sequence in context: A041421 A042742 A144350 * A158672 A268948 A276396

Adjacent sequences: A111213 A111214 A111215 * A111217 A111218 A111219

Keyword

nonn,easy

Author

N. J. A. Sloane, following a suggestion from R. K. Guy, Oct 26 2005

Status

approved