A154239 a(n) = ( (7 + sqrt(6))^n - (7 - sqrt(6))^n )/(2*sqrt(6)).

1, 14, 153, 1540, 14981, 143514, 1365013, 12939080, 122451561, 1157941414, 10945762673, 103449196620, 977620957741, 9238377953714, 87299590169133, 824944010358160, 7795333767741521, 73662080302980414, 696069772228840393

Offset

1,2

Comments

lim_{n -> infinity} a(n)/a(n-1) = 7 + sqrt(6) = 9.4494897427....

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (14, -43).

Formula

From Philippe Deléham, Jan 06 2009: (Start)

a(n) = 14*a(n-1) - 43*a(n-2)for n>1, with a(0)=0, a(1)=1.

G.f.: x/(1 - 14x + 43x^2). (End)

E.g.f.: sinh(sqrt(6)*x)*exp(7*x)/sqrt(6). - Ilya Gutkovskiy, Sep 07 2016

Mathematica

Join[{a=1, b=14}, Table[c=14*b-43*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
LinearRecurrence[{14, -43}, {1, 14}, 25] (* or *) Table[( (7 + sqrt(6))^n - (7 - sqrt(6))^n )/(2*sqrt(6)), {n, 1, 25}] (* G. C. Greubel, Sep 07 2016 *)

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-6); S:=[ ((7+r)^n-(7-r)^n)/(2*r): n in [1..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 07 2009
I:=[1, 14]; [n le 2 select I[n] else 14*Self(n-1)-43*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Sep 07 2016

Crossrefs

Cf. A010464 (decimal expansion of square root of 6).

Sequence in context: A222677 A016163 A153884 * A016215 A329711 A290675

Adjacent sequences: A154236 A154237 A154238 * A154240 A154241 A154242

Keyword

nonn

Author

Al Hakanson (hawkuu(AT)gmail.com), Jan 05 2009

Extensions

Extended beyond a(7) by Klaus Brockhaus, Jan 07 2009

Edited by Klaus Brockhaus, Oct 06 2009

Status

approved