A156156 a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1) = 13, a(2) = 53.

13, 53, 305, 1777, 10357, 60365, 351833, 2050633, 11951965, 69661157, 406014977, 2366428705, 13792557253, 80388914813, 468540931625, 2730856674937, 15916599117997, 92768738033045, 540695829080273, 3151406236448593

Offset

1,1

Comments

lim_{n -> infinity} a(n)/a(n-1) = 3+2*sqrt(2).

Links

Table of n, a(n) for n=1..20.

Index entries for linear recurrences with constant coefficients, signature (6, -1).

Formula

a(n) = ((50+31*sqrt(2))*(3-2*sqrt(2))^n+(50-31*sqrt(2))*(3+2*sqrt(2))^n)/4.

G.f.: x*(13-25*x)/(1-6*x+x^2).

Prog

(PARI) {m=20; v=concat([13, 53], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-v[n-2]); v}

Crossrefs

First trisection of A155923.

Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156157, A156158.

Sequence in context: A142188 A248409 A206444 * A201486 A176617 A254895

Adjacent sequences: A156153 A156154 A156155 * A156157 A156158 A156159

Keyword

nonn

Author

Klaus Brockhaus, Feb 09 2009

Extensions

Replaced abbreviation by sqrt(2) Klaus Brockhaus, Feb 12 2009

G.f. corrected by Klaus Brockhaus, Sep 23 2009

Status

approved