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A156574 a(n) = 34*a(n-1)-a(n-2)-4232 for n > 2; a(1)=1369, a(2)=42025. 3
1369, 42025, 1423249, 48344209, 1642275625, 55789022809, 1895184495649, 64380483825025, 2187041265550969, 74295022544903689, 2523843725261170225, 85736391636334879729, 2912513471910124736329, 98939721653307906151225 (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) = (1058+(627-238*sqrt(2))*(17+12*sqrt(2))^n+(627+238*sqrt(2))*(17-12*sqrt(2))^n)/8.

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

EXAMPLE

a(3) = 34*a(2)-a(1)-4232 = 34*42025-1369-4232 = 1423249.

PROG

(PARI) {m=14; v=concat([1369, 42025], vector(m-2)); for(n=3, m, v[n]=34*v[n-1]-v[n-2]-4232); v}

CROSSREFS

Third trisection of A156572.

Cf. A156164 (decimal expansion of 17+12*sqrt(2)), A156573, A156575.

Sequence in context: A221932 A331464 A167724 * A145697 A045107 A031752

Adjacent sequences:  A156571 A156572 A156573 * A156575 A156576 A156577

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 July 26 10:21 EDT 2021. Contains 346294 sequences. (Running on oeis4.)