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A156573 a(n) = 34*a(n-1)-a(n-2)-4232 for n > 2; a(1)=529, a(2)=13225. 3
529, 13225, 444889, 15108769, 513249025, 17435353849, 592288777609, 20120383080625, 683500735959409, 23218904639535049, 788759257008228025, 26794595833640213569, 910227499086759029089, 30920940373116166771225 (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

Table of n, a(n) for n=1..14.

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

FORMULA

a(n) = 529*(2+(3-2*sqrt(2))*(17+12*sqrt(2))^n+(3+2*sqrt(2))*(17-12*sqrt(2))^n)/8.

G.f.: 529*x*(1-10*x+x^2)/((1-x)*(1-34*x+x^2)).

EXAMPLE

a(3) = 34*a(2)-a(1)-4232 = 34*13225-529-4232 = 444889.

PROG

(PARI) {m=14; v=concat([529, 13225], vector(m-2)); for(n=3, m, v[n]=34*v[n-1]-v[n-2]-4232); v}

CROSSREFS

Second trisection of A156572. Equals 529*A008844.

Cf. A156164 (decimal expansion of 17+12*sqrt(2)), A156574, A156575.

Sequence in context: A067475 A052074 A112079 * A034987 A206861 A206955

Adjacent sequences:  A156570 A156571 A156572 * A156574 A156575 A156576

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 August 1 17:43 EDT 2021. Contains 346402 sequences. (Running on oeis4.)