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A156158 a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1) = 25, a(2) = 137. 4
25, 137, 797, 4645, 27073, 157793, 919685, 5360317, 31242217, 182092985, 1061315693, 6185801173, 36053491345, 210135146897, 1224757390037, 7138409193325, 41605697769913, 242495777426153, 1413368966787005 (list; graph; refs; listen; history; text; internal format)
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..19.

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

FORMULA

a(n) = ((26+7*sqrt(2))*(3-2*sqrt(2))^n+(26-7*sqrt(2))*(3+2*sqrt(2))^n)/4.

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

MATHEMATICA

LinearRecurrence[{6, -1}, {25, 137}, 30] (* Harvey P. Dale, Jan 02 2019 *)

PROG

(PARI) {m=19; v=concat([25, 137], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-v[n-2]); v}

CROSSREFS

Third trisection of A155923.

Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156156, A156157.

Sequence in context: A305956 A317217 A147489 * A195977 A233368 A240415

Adjacent sequences:  A156155 A156156 A156157 * A156159 A156160 A156161

KEYWORD

nonn,easy

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

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Last modified May 25 07:08 EDT 2020. Contains 334584 sequences. (Running on oeis4.)