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A156575 a(n) = 34*a(n-1)-a(n-2)-4232 for n > 2; a(1)=289, a(2)=4225. 4
289, 4225, 139129, 4721929, 160402225, 5448949489, 185103876169, 6288082836025, 213609712544449, 7256442143671009, 246505423172265625, 8373927945713356009, 284467044731081834449, 9663505592911069011025 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

lim_{n -> infinity} a(n)/a(n-1) = 17+12*sqrt(2).

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..600

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

FORMULA

a(n) = (1058 + (4947 - 3478*sqrt(2))*(17 + 12*sqrt(2))^n + (4947 + 3478*sqrt(2))*(17 - 12*sqrt(2))^n)/8.

G.f.: x*(289 -5890*x +1369*x^2)/((1-x)*(1-34*x+x^2)).

a(1)=289, a(2)=4225, a(3)=139129, a(n) = 35*a(n-1) - 35*a(n-2) + a(n-3). - Harvey P. Dale, Dec 15 2011

a(n) = -1369*[n=0] + (529/4) + (3/4)*(1649*ChebyshevU(n, 17) - 55857*ChebyshevU(n-1, 17)). - G. C. Greubel, Jan 04 2022

EXAMPLE

a(4) = 34*a(3) -a(2) -4232 = 34*139129 -4225 -4232 = 4721929.

MATHEMATICA

RecurrenceTable[{a[1]==289, a[2]==4225, a[n]==34a[n-1]-a[n-2]-4232}, a, {n, 20}] (* or *) LinearRecurrence[{35, -35, 1}, {289, 4225, 139129}, 20] (* Harvey P. Dale, Dec 15 2011 *)

PROG

(PARI) {m=14; v=concat([289, 4225], vector(m-2)); for(n=3, m, v[n]=34*v[n-1]-v[n-2]-4232); v}

(Sage)

def a(n): return -1369*bool(n==0) + (529/4) + (3/4)*(1649*chebyshev_U(n, 17) - 55857*chebyshev_U(n-1, 17))

[a(n) for n in (1..30)] # G. C. Greubel, Jan 04 2022

CROSSREFS

First trisection of A156572.

Cf. A156164 (decimal expansion of 17+12*sqrt(2)), A156573, A156574.

Sequence in context: A112077 A152934 A332737 * A296404 A156161 A114762

Adjacent sequences:  A156572 A156573 A156574 * A156576 A156577 A156578

KEYWORD

nonn,easy

AUTHOR

Klaus Brockhaus, Feb 11 2009

EXTENSIONS

Revised by Klaus Brockhaus, Feb 16 2009

G.f. corrected by Klaus Brockhaus, Sep 22 2009

STATUS

approved

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Last modified September 26 08:43 EDT 2022. Contains 356993 sequences. (Running on oeis4.)