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A157877 Expansion of (1-x)*x/(x^2-30*x+1). 6
1, 29, 869, 26041, 780361, 23384789, 700763309, 20999514481, 629284671121, 18857540619149, 565096933903349, 16934050476481321, 507456417360536281, 15206758470339607109, 455695297692827676989, 13655652172314490702561, 409213869871741893399841 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence is part of a solution of a more general problem involving 2 equations, three sequences a(n), b(n), c(n) and a constant A:

    A    * c(n)+1 = a(n)^2,

   (A+1) * c(n)+1 = b(n)^2, for details see comment in A157014.

A157877 is the a(n) sequence for A=7.

Positive values of x (or y) satisfying x^2 - 30xy + y^2 + 28 = 0. - Colin Barker, Feb 23 2014

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (30,-1).

FORMULA

G.f.: (1-x)*x/(x^2-30*x+1).

a(1)=1, a(2)=29; for n>2, a(n) = 30*a(n-1)-a(n-2).

7*A157879(n)+1 = a(n)^2.

8*A157879(n)+1 = A157878(n)^2.

a(n) = (1/8)*(4-sqrt(14))*(1+(15+4*sqrt(14))^(2*n-1))/(15+4*sqrt(14))^(n-1). - Bruno Berselli, Feb 25 2014

MATHEMATICA

q=7; s=0; lst={}; Do[s+=n; If[Sqrt[q*s+1] == Floor[Sqrt[q*s+1]], AppendTo[lst, Sqrt[q*s+1]]], {n, 0, 9!}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 02 2009 *)

LinearRecurrence[{30, -1}, {1, 29}, 30] (* Harvey P. Dale, Dec 14 2011 *)

CoefficientList[Series[(1 - x)/(x^2 - 30 x + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 25 2014 *)

PROG

(PARI) Vec((1-x)*x/(x^2-30*x+1)+O(x^99)) \\ Charles R Greathouse IV, Sep 25 2012

(MAGMA) I:=[1, 29, 869]; [n le 3 select I[n] else 30*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Feb 25 2014

CROSSREFS

Cf. A157879, A157877, A157878.

Cf. similar sequences listed in A238379.

Sequence in context: A057687 A049667 A042626 * A158665 A167738 A107964

Adjacent sequences:  A157874 A157875 A157876 * A157878 A157879 A157880

KEYWORD

nonn,easy

AUTHOR

Paul Weisenhorn, Mar 08 2009

EXTENSIONS

Edited by Alois P. Heinz, Sep 09 2011

STATUS

approved

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Last modified February 24 11:39 EST 2018. Contains 299603 sequences. (Running on oeis4.)