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URL: https://oeis.org/A154239

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A154239
a(n) = ( (7 + sqrt(6))^n - (7 - sqrt(6))^n )/(2*sqrt(6)).
1
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....
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
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