A154248 a(n) = ( (7 + sqrt(7))^n - (7 - sqrt(7))^n )/(2*sqrt(7)).

1, 14, 154, 1568, 15484, 150920, 1462552, 14137088, 136492048, 1317130976, 12707167648, 122580846080, 1182430803904, 11405635719296, 110016806306176, 1061198588076032, 10236074368205056, 98734700455677440

Offset

1,2

Comments

Lim_{n -> infinity} a(n)/a(n-1) = 7 + sqrt(7) = 9.6457513110....

Links

G. C. Greubel, Table of n, a(n) for n = 1..750

Index entries for linear recurrences with constant coefficients, signature (14,-42).

Formula

From Philippe Deléham, Jan 06 2009: (Start)

a(n) = 14*a(n-1) - 42*a(n-2) for n>1, with a(0)=0, a(1)=1.

G.f.: x/(1 - 14x + 42x^2). (End)

E.g.f.: (1/sqrt(7))*exp(7*x)*sinh(sqrt(7)*x). - G. C. Greubel, Sep 08 2016

Maple

a:= n-> (<<0|1>, <-42|14>>^n)[1, 2]:
seq(a(n), n=0..25);  # Alois P. Heinz, Dec 22 2013

Mathematica

Join[{a=1, b=14}, Table[c=14*b-42*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
LinearRecurrence[{14, -42}, {1, 14}, 25] (* or *) Table[( (7 + sqrt(7))^n - (7 - sqrt(7))^n )/(2*sqrt(7)), {n, 1, 25}] (* G. C. Greubel, Sep 08 2016 *)

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-7); S:=[ ((7+r)^n-(7-r)^n)/(2*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 07 2009

Crossrefs

Cf. A010465 (decimal expansion of square root of 7).

Sequence in context: A257288 A125426 A004986 * A006865 A263474 A154347

Adjacent sequences: A154245 A154246 A154247 * A154249 A154250 A154251

Keyword

nonn,easy

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