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A280931 a(n) = 2*F(n-1) + 9*F(n-4) + 9*F(n-7) where n >= 7 and F = A000045.

%I A280931 #42 Jan 05 2025 19:51:41
%S A280931 34,62,96,158,254,412,666,1078,1744,2822,4566,7388,11954,19342,31296,
%T A280931 50638,81934,132572,214506,347078,561584,908662,1470246,2378908,
%U A280931 3849154,6228062,10077216,16305278,26382494,42687772,69070266,111758038,180828304,292586342
%N A280931 a(n) = 2*F(n-1) + 9*F(n-4) + 9*F(n-7) where n >= 7 and F = A000045.
%H A280931 Vincenzo Librandi, <a href="/A280931/b280931.txt">Table of n, a(n) for n = 7..1100</a>
%H A280931 H. Zhao and X. Li, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/44-1/quarthzhoa01_2006.pdf">On the Fibonacci numbers of trees</a>, The Fibonacci Quarterly, Vol. 44, Number 1 (2006), page 37.
%H A280931 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).
%F A280931 G.f.: 2*x^7*(17 + 14*x)/(1 - x - x^2).
%F A280931 a(n) = a(n-1) + a(n-2).
%F A280931 From the g.f.: a(n) = 34*F(n-6) + 28*F(n-7) = 28*F(n-5) + 6*F(n-6) = 6*F(n-4) + 22*F(n-5) = 22*F(n-3) - 16*F(n-4) = -16*F(n-2) + 38*F(n-3) = 38*F(n-1) - 54*F(n-2) = -54*F(n) + 92*F(n-1), and so on.
%F A280931 a(n) = 2*A022125(n-5).
%F A280931 a(n) = F(n+2) + F(n-3) + F(n-11). - _Greg Dresden_, Jul 07 2022
%t A280931 LinearRecurrence[{1, 1}, {34, 62}, 35]
%o A280931 (Magma) [2*Fibonacci(n-1)+9*Fibonacci(n-4)+9*Fibonacci(n-7): n in [7..40]];
%o A280931 (Magma) a0:=34; a1:=62; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..40]];
%Y A280931 Cf. A000045, A022125, A022130, A101156, A280932.
%K A280931 nonn,easy
%O A280931 7,1
%A A280931 _Vincenzo Librandi_, Jan 24 2017
%E A280931 Corrected and extended by _Bruno Berselli_, Jan 24 2017