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

Author

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

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A049685.

Cf. similar sequences listed in A238379.

Programs

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

Mathematica

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

PARI

Vec((1-x)/(1-31*x+x^2) + O(x^100)) \\ Colin Barker, Feb 24 2014

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