|
%I #42 Jun 13 2015 00:53:53
%S 0,0,0,0,1,1,5,6,18,24,57,81,169,250,482,732,1341,2073,3669,5742,9922,
%T 15664,26609,42273,70929,113202,188226,301428,497845,799273,1313501,
%U 2112774,3459042,5571816,9096393,14668209
%N a(n) = Fibonacci(n-2) + 2*a(n-2) - (n mod 2).
%C The sequence is Fibonacci-like in the sense that a(n)/a(n-1) converges to the golden ratio as n goes to infinity.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-3,-5,2,2).
%F a(n) = Fibonacci(n-2) + 2*a(n-2) - n mod 2 for all n >= 2, with a(0) = a(1) = 0.
%F G.f.: -x^4 / ( (x-1)*(1+x)*(2*x^2-1)*(x^2+x-1) ). - _R. J. Mathar_, Jul 09 2011
%F a(n) = A000045(n+1) + A000035(n) - A016116(n+1). - _R. J. Mathar_, Jul 09 2011
%e a(10) = is Fibonacci(8) + 2*a(8) - (10 mod 2) = 21 + 36 - 0 = 57.
%o (PARI) a(n) = if (n<=2, 0, fibonacci(n-2) + 2*a(n-2) - n % 2); \\ _Michel Marcus_, Aug 29 2013
%K nonn,easy
%O 0,7
%A _Derek Devine_, Jul 08 2011
|
