This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A023550 #24 Nov 25 2024 17:55:43
%S A023550 2,7,16,32,59,104,178,299,496,816,1335,2176,3538,5743,9312,15088,
%T A023550 24435,39560,64034,103635,167712,271392,439151,710592,1149794,1860439,
%U A023550 3010288,4870784,7881131,12751976,20633170,33385211,54018448,87403728,141422247,228826048
%N A023550 Convolution of natural numbers >= 2 and (F(2), F(3), F(4), ...).
%H A023550 Vincenzo Librandi, <a href="/A023550/b023550.txt">Table of n, a(n) for n = 1..1000</a>
%H A023550 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3, -2, -1, 1).
%F A023550 a(n) = A023537(n) + 2*n.
%F A023550 From _Colin Barker_, Mar 11 2017: (Start)
%F A023550 G.f.: x*(2-x)*(1+x) / ((1-x)^2*(1-x-x^2)).
%F A023550 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 A023550 a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4) for n>4.
%F A023550 (End)
%F A023550 a(n) = Lucas(n+4) - 2*n - 7. - _G. C. Greubel_, Jun 01 2019
%t A023550 LinearRecurrence[{3,-2,-1,1}, {2,7,16,32}, 40] (* _Vladimir Joseph Stephan Orlovsky_, Feb 11 2012 *)
%o A023550 (PARI) Vec(x*(2-x)*(1+x)/((1-x)^2*(1-x-x^2)) + O(x^40)) \\ _Colin Barker_, Mar 11 2017
%o A023550 (PARI) vector(40, n, fibonacci(n+5) + fibonacci(n+3) -2*n-7) \\ _G. C. Greubel_, Jun 01 2019
%o A023550 (Magma) [Lucas(n+4) - 2*n - 7 : n in [1..40]]; // _G. C. Greubel_, Jun 01 2019
%o A023550 (Sage) [lucas_number2(n+4,1,-1) -2*n-7 for n in (1..40)] # _G. C. Greubel_, Jun 01 2019
%o A023550 (GAP) List([1..40], n-> Lucas(1, -1, n+4)[2] -2*n-7 ); # _G. C. Greubel_, Jun 01 2019
%Y A023550 Cf. A000032, A023537.
%K A023550 nonn,easy
%O A023550 1,1
%A A023550 _Clark Kimberling_