%I #21 Sep 08 2022 08:44:47
%S 2,7,16,32,59,104,178,299,496,816,1335,2176,3538,5743,9312,15088,
%T 24435,39560,64034,103635,167712,271392,439151,710592,1149794,1860439,
%U 3010288,4870784,7881131,12751976,20633170,33385211,54018448,87403728,141422247,228826048
%N Convolution of natural numbers >= 2 and (F(2), F(3), F(4), ...).
%H Vincenzo Librandi, <a href="/A023550/b023550.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3, -2, -1, 1).
%F a(n) = A023537(n) + 2*n.
%F From _Colin Barker_, Mar 11 2017: (Start)
%F G.f.: x*(2-x)*(1+x) / ((1-x)^2*(1-x-x^2)).
%F a(n) = (2^(-1-n)*((1-sqrt(5))^n*(-15+7*sqrt(5)) + (1+sqrt(5))^n*(15+7*sqrt(5)))) / sqrt(5) - 2*n - 7.
%F a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4) for n>4.
%F (End)
%F a(n) = Lucas(n+4) - 2*n - 7. - _G. C. Greubel_, Jun 01 2019
%t LinearRecurrence[{3,-2,-1,1}, {2,7,16,32}, 40] (* _Vladimir Joseph Stephan Orlovsky_, Feb 11 2012 *)
%o (PARI) Vec(x*(2-x)*(1+x)/((1-x)^2*(1-x-x^2)) + O(x^40)) \\ _Colin Barker_, Mar 11 2017
%o (PARI) vector(40, n, fibonacci(n+5) + fibonacci(n+3) -2*n-7) \\ _G. C. Greubel_, Jun 01 2019
%o (Magma) [Lucas(n+4) - 2*n - 7 : n in [1..40]]; // _G. C. Greubel_, Jun 01 2019
%o (Sage) [lucas_number2(n+4,1,-1) -2*n-7 for n in (1..40)] # _G. C. Greubel_, Jun 01 2019
%o (GAP) List([1..40], n-> Lucas(1, -1, n+4)[2] -2*n-7 ) # _G. C. Greubel_, Jun 01 2019
%Y Cf. A000032, A023537.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_