A155464 a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3) for n > 2; a(0) = 0, a(1) = 51, a(2) = 340.

0, 51, 340, 2023, 11832, 69003, 402220, 2344351, 13663920, 79639203, 464171332, 2705388823, 15768161640, 91903581051, 535653324700, 3122016367183, 18196444878432, 106056652903443, 618143472542260, 3602804182350151

Offset

0,2

Comments

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

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,-7,1).

Formula

a(n) = 6*a(n-1) - a(n-2) + 34 for n > 1; a(0) = 0, a(1) = 51.

a(n) = ((1+sqrt(2))*(3+2*sqrt(2))^n + (1-sqrt(2))*(3-2*sqrt(2))^n -2)*(17/4).

G.f.: 17*x*(3-x)/((1-x)*(1-6*x+x^2)).

a(n) = 17*(A002203(2*n+1) - 2)/4. - G. C. Greubel, Aug 21 2018

Mathematica

LinearRecurrence[{7, -7, 1}, {0, 51, 340}, 30] (* Harvey P. Dale, Jun 10 2013 *)
Table[17*(LucasL[2*n+1, 2] - 2)/4, {n, 0, 50}] (* G. C. Greubel, Aug 21 2018 *)

Prog

(PARI) {m=20; v=concat([0, 51, 340], vector(m-3)); for(n=4, m, v[n]=7*v[n-1]-7*v[n-2]+v[n-3]); v}
(Magma) I:=[0, 51, 340]; [n le 3 select I[n] else 7*Self(n-1) - 7*Self(n-2) + Self(n-3): n in [1..30]]; // G. C. Greubel, Aug 21 2018

Crossrefs

First trisection of A118120. Equals 17*A001652.

Cf. A155465, A155466, A156035 (decimal expansion of 3+2*sqrt(2)).

Sequence in context: A251344 A245362 A219145 * A165087 A359026 A152579

Adjacent sequences: A155461 A155462 A155463 * A155465 A155466 A155467

Keyword

nonn,easy

Author

Klaus Brockhaus, Jan 30 2009

Extensions

Comment and recursion formula added, cross-references edited by Klaus Brockhaus, Sep 23 2009

Status

approved