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 A354855 #48 Jun 14 2022 01:41:18 %S A354855 0,4,35,228,1287,6820,34667,171332,829455,3952836,18604979,86693156, %T A354855 400623383,1838490212,8387044091,38065809540,171999313951, %U A354855 774138335108,3472202765123,15525625108324,69229056160039,307921937307684,1366491508589195,6051666872017348 %N A354855 a(n) = floor(n*(2+sqrt(5))^n), equivalently, floor(n*phi^(3n)), where phi = (1+sqrt(5))/2 is the golden ratio. %H A354855 Stefano Spezia, <a href="/A354855/b354855.txt">Table of n, a(n) for n = 0..1500</a> %H A354855 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (8,-13,-16,13,8,1). %F A354855 a(n) = floor((2+sqrt(5))^n*n). %F A354855 a(n) = floor(n*phi^(3n)) where phi=(1+sqrt(5))/2 is the golden ratio. %F A354855 a(n) = floor(n*F(3n-1)+n*phi*F(3n)), where F(n) = A000045(n) is the n-th Fibonacci number. %F A354855 a(n) = n*L(3n) when n is odd and a(n) = n*L(3n)-1 when n is even (n>=2), where L(n) = A000032(n) is the n-th Lucas number. %F A354855 G.f.: x*(4 + 3*x - 18*x^3 - 4*x^4 - x^5)/((1 - x)*(1 + x)*(1 - 4*x - x^2)^2). - _Stefano Spezia_, Jun 12 2022 %t A354855 a[n_] := Floor[n * GoldenRatio^(3*n)]; Array[a, 25, 0] (* _Amiram Eldar_, Jun 09 2022 *) %Y A354855 Cf. A000032, A000045, A001622, A004976, A098317, A128439. %K A354855 nonn,easy %O A354855 0,2 %A A354855 _Jiale Wang_, Jun 09 2022