%I #33 Sep 08 2022 08:45:16

%S 10,24,34,58,92,150,242,392,634,1026,1660,2686,4346,7032,11378,18410,

%T 29788,48198,77986,126184,204170,330354,534524,864878,1399402,2264280,

%U 3663682,5927962,9591644,15519606,25111250,40630856,65742106,106372962,172115068

%N a(n) = 2*Fibonacci(n) + 8*Fibonacci(n-5).

%H Colin Barker, <a href="/A101156/b101156.txt">Table of n, a(n) for n = 5..1000</a>

%H H. Zhao and X. Li, <a href="http://www.fq.math.ca/Papers1/44-1/quarthzhoa01_2006.pdf">On the Fibonacci numbers of trees</a>, Fib. Quart., 44 (2006), 32-38.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).

%F From _Colin Barker_, Jul 30 2013: (Start)

%F a(n) = a(n-1) + a(n-2).

%F G.f.: -2*x^5*(7*x+5) / (x^2+x-1). (End)

%p with(combinat): A101156:=n->2*fibonacci(n)+8*fibonacci(n-5): seq(A101156(n), n=5..50); # _Wesley Ivan Hurt_, Jan 23 2017

%t Table[2Fibonacci[n]+8Fibonacci[n-5],{n,5,40}] (* _Harvey P. Dale_, Jul 15 2013 *)

%t LinearRecurrence[{1, 1}, {10, 24}, 35] (* _Vincenzo Librandi_, Jan 24 2017 *)

%o (PARI) Vec(-2*x^5*(7*x+5)/(x^2+x-1) + O(x^50)) \\ _Colin Barker_, Mar 07 2016

%o (Magma) [2*Fibonacci(n)+8*Fibonacci(n-5): n in [5..40]]; // _Vincenzo Librandi_, Jan 24 2017

%K nonn,easy

%O 5,1

%A _N. J. A. Sloane_, Oct 03 2007