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a(0)=1, a(n) = 2*Fibonacci(n+4) - 6.
1

%I #18 Jul 02 2023 17:49:00

%S 1,4,10,20,36,62,104,172,282,460,748,1214,1968,3188,5162,8356,13524,

%T 21886,35416,57308,92730,150044,242780,392830,635616,1028452,1664074,

%U 2692532,4356612,7049150,11405768,18454924,29860698,48315628,78176332,126491966

%N a(0)=1, a(n) = 2*Fibonacci(n+4) - 6.

%D P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 158.

%H Harry J. Smith, <a href="/A063758/b063758.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2, 0, -1).

%F G.f.: (1+2*x+2*x^2+x^3)/((1-x-x^2)*(1-x)).

%p seq(`if`(n=0, 1, 2*combinat[fibonacci](n+4)-6), n=0..35); # _Nathaniel Johnston_, Jun 28 2011

%t Table[If[n == 0, 1, 2*Fibonacci[n + 4] - 6], {n, 0, 100}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 28 2011 *)

%o (PARI) { for (n=0, 500, if (n, a=2*fibonacci(n+4) - 6, a=1); write("b063758.txt", n, " ", a) ) } \\ _Harry J. Smith_, Aug 29 2009

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Aug 14 2001