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A067977 Convolution of Fibonacci F(n+1), n>=0, with F(n+9), n>=0.

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%I A067977 #10 Dec 22 2022 18:47:53
%S A067977 34,89,212,445,890,1712,3212,5911,10720,19215,34116,60096,105158,
%T A067977 182965,316780,546113,937918,1605424,2739760,4662995,7916984,13412019,
%U A067977 22675272,38265600,64465450,108433937
%N A067977 Convolution of Fibonacci F(n+1), n>=0, with F(n+9), n>=0.
%C A067977 Ninth diagonal of A067330. Ninth column of A067418.
%H A067977 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2,-1).
%F A067977 a(n) = A067330(n+8, n) = A067418(n+8, 8) = Sum_{k=0..n} F(k+1)*F(n+9-k), n>=0.
%F A067977 G.f.: (34+21*x)/(1-x-x^2)^2.
%F A067977 a(n) = ((123*n+5*34)*F(n+1)+76*(n+1)*F(n))/5, F(n) := A000045(n) (Fibonacci); 34=F(9), 76=L(9), 123=L(10), L(n) := A000204(n) (Lucas).
%t A067977 CoefficientList[Series[(34 + 21*x)/(1 - x - x^2)^2, {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Feb 16 2017 *)
%t A067977 LinearRecurrence[{2,1,-2,-1},{34,89,212,445},30] (* _Harvey P. Dale_, Dec 22 2022 *)
%Y A067977 Cf. A000045, A000204, A067330, A067418.
%K A067977 nonn,easy
%O A067977 0,1
%A A067977 _Wolfdieter Lang_, Feb 15 2002