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A029546 Expansion of 1/(1 - 35*x + 35*x^2 - x^3). 11
1, 35, 1190, 40426, 1373295, 46651605, 1584781276, 53835911780, 1828836219245, 62126595542551, 2110475412227490, 71694037420192110, 2435486796874304251, 82734857056306152425, 2810549653117534878200, 95475953348939879706376, 3243371864210838375138585 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Numbers m such that r = 24*m+1 and 2*r-1 are both squares. - Bruno Berselli, Jul 17 2014

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (35,-35,1).

FORMULA

a(n) = A029549(n+1)/6 = A075528(n+1)/3.

From Colin Barker, Mar 02 2016: (Start)

a(n) = 35*a(n-1)-35*a(n-2)+a(n-3) for n>2.

a(n) = ((17+12*sqrt(2))^(-n)*(99-70*sqrt(2)-6*(17+12*sqrt(2))^n+(17+12*sqrt(2))^(2*n)*(99+70*sqrt(2))))/192. (End)

MATHEMATICA

LinearRecurrence[{35, -35, 1}, {1, 35, 1190}, 20] (* Vincenzo Librandi, Nov 22 2011 *)

PROG

(MAGMA) I:=[1, 35, 1190]; [n le 3 select I[n] else 35*Self(n-1)-35*Self(n-2)+Self(n-3): n in [1..20]]; // Vincenzo Librandi, Nov 22 2011

(PARI) Vec(1/(1-35*x+35*x^2-x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012

CROSSREFS

Cf. A029547 (first differences), A245031 (see Comments line).

Sequence in context: A046176 A162847 * A305539 A163218 A163600 A164068

Adjacent sequences:  A029543 A029544 A029545 * A029547 A029548 A029549

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified August 18 17:55 EDT 2018. Contains 313834 sequences. (Running on oeis4.)