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A280932 a(n) = 2*F(n-1) + 2*F(n-3) + 10*F(n-5) + 9*F(n-8) where n >= 8 and F = A000045.

%I A280932 #35 Jan 05 2025 19:51:41
%S A280932 56,97,153,250,403,653,1056,1709,2765,4474,7239,11713,18952,30665,
%T A280932 49617,80282,129899,210181,340080,550261,890341,1440602,2330943,
%U A280932 3771545,6102488,9874033,15976521,25850554,41827075,67677629,109504704,177182333,286687037
%N A280932 a(n) = 2*F(n-1) + 2*F(n-3) + 10*F(n-5) + 9*F(n-8) where n >= 8 and F = A000045.
%H A280932 Vincenzo Librandi, <a href="/A280932/b280932.txt">Table of n, a(n) for n = 8..1100</a>
%H A280932 H. Zhao and X. Li, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/44-1.html">On the Fibonacci numbers of trees</a>, The Fibonacci Quarterly, Vol. 44, Number 1 (2006), page 37.
%H A280932 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).
%F A280932 G.f.: x^8*(56 + 41*x)/(1 - x - x^2).
%F A280932 a(n) = a(n-1) + a(n-2).
%F A280932 From the g.f.: a(n) = 56*F(n-7) + 41*F(n-8) = 41*F(n-6) + 15*F(n-7) = 15*F(n-5) + 26*F(n-6) = 26*F(n-4) - 11*F(n-5) = -11*F(n-3) + 37*F(n-4) = 37*F(n-2) - 48*F(n-3) = -48*F(n-1) + 85*F(n-2) = 85*F(n) - 133*F(n-1), and so on.
%t A280932 LinearRecurrence[{1, 1}, {56, 97}, 35]
%o A280932 (Magma) [2*Fibonacci(n-1)+2*Fibonacci(n-3)+10*Fibonacci(n-5)+9*Fibonacci(n-8): n in [8..40]];
%o A280932 (Magma) a0:=56; a1:=97; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..40]];
%Y A280932 Cf. A000045, A022130, A101156, A280931.
%K A280932 nonn,easy
%O A280932 8,1
%A A280932 _Vincenzo Librandi_, Jan 24 2017
%E A280932 Corrected and extended by _Bruno Berselli_, Jan 24 2017