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 A213577 #18 May 09 2025 19:52:12
%S A213577 1,4,17,56,172,498,1395,3820,10307,27534,73064,193012,508341,1336132,
%T A213577 3507189,9197732,24107124,63159782,165433895,433246860,1134484871,
%U A213577 2970509594,7777554192,20363014056,53312938537,139578241348
%N A213577 Principal diagonal of the convolution array A213576.
%H A213577 Clark Kimberling, <a href="/A213577/b213577.txt">Table of n, a(n) for n = 1..1000</a>
%H A213577 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (5,-6,-3,6,1,-1).
%F A213577 a(n) = 5*a(n-1) - 6*a(n-2) - 3*a(n-3) + 6*a(n-4) + a(n-5) - a(n-6).
%F A213577 G.f.: x*(1 - x + 3*x^2 - 2*x^3)/((1 - 3*x + x^2)*(1 - x - x^2)^2).
%F A213577 a(n) = Fibonacci(2*n+3) - Fibonacci(n+3) - n*Fibonacci(n+1). - _G. C. Greubel_, Jul 05 2019
%t A213577 (See A213576.)
%t A213577 LinearRecurrence[{5,-6,-3,6,1,-1},{1,4,17,56,172,498},30] (* _Harvey P. Dale_, Aug 23 2012 *)
%t A213577 Table[Fibonacci[2n+3] -Fibonacci[n+3] -n*Fibonacci[n+1], {n,1,40}] (* _G. C. Greubel_, Jul 05 2019 *)
%o A213577 (PARI) vector(40, n, fibonacci(2*n+3) - fibonacci(n+3) - n*fibonacci(n+1)) \\ _G. C. Greubel_, Jul 05 2019
%o A213577 (Magma) [Fibonacci(2*n+3) -Fibonacci(n+3) -n*Fibonacci(n+1): n in [1..40]]; // _G. C. Greubel_, Jul 05 2019
%o A213577 (Sage) [fibonacci(2*n+3) - fibonacci(n+3) - n*fibonacci(n+1) for n in (1..40)] # _G. C. Greubel_, Jul 05 2019
%o A213577 (GAP) List([1..40], n-> Fibonacci(2*n+3) - Fibonacci(n+3) - n*Fibonacci(n+1)); # _G. C. Greubel_, Jul 05 2019
%Y A213577 Cf. A213576, A213500.
%K A213577 nonn,easy
%O A213577 1,2
%A A213577 _Clark Kimberling_, Jun 18 2012