A060160 - OEIS

%I #16 Dec 25 2024 15:49:49

%S 1,11,23,79,223,703,2175,6911,22015,70655,227327,733183,2367487,

%T 7651327,24739839,80019455,258867199,837550079,2710044671,8769241087,

%U 28376563711,91825897471,297149661183,961586135039,3111737360383,10069752152063

%N a(n) = 2^n - 1 + Fibonacci(n-1)*2^(n+1).

%H Harry J. Smith, <a href="/A060160/b060160.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5, -4, -8, 8).

%F From _R. J. Mathar_, Feb 06 2010: (Start)

%F a(n) = 5*a(n-1) - 4*a(n-2) - 8*a(n-3) + 8*a(n-4).

%F G.f.: x*(1+6*x-28*x^2+16*x^3)/ ((1-x) * (2*x-1) * (4*x^2+2*x-1)). (End)

%p with(combinat, fibonacci): seq(2^n - 1 + fibonacci(n - 1)*2^(n+1), n=1..25);

%t Table[2^n-1+Fibonacci[n-1]2^(n+1),{n,30}] (* or *) LinearRecurrence[{5,-4,-8,8},{1,11,23,79},30] (* _Harvey P. Dale_, Dec 19 2021 *)

%o (PARI) a(n) = { 2^n - 1 + fibonacci(n - 1)*2^(n + 1) } \\ _Harry J. Smith_, Jul 02 2009

%Y Cf. A060161, A000045 (Fibonacci).

%K nonn

%O 1,2

%A Pieter Gosselink (pieter_gosselink(AT)lotus.com), Mar 12 2001

%E More terms from _Asher Auel_, Mar 16 2001