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 A382641 #17 Apr 02 2025 05:06:35
%S A382641 1,1,2,3,5,7,10,15,21,31,46,67,98,144,211,309,453,664,973,1426,2090,
%T A382641 3063,4489,6579,9642,14131,20710,30352,44483,65193,95545,140028,
%U A382641 205221,300766,440794,646015,946781,1387575,2033590,2980371,4367946,6401536,9381907,13749853
%N A382641 a(n) = round(c^n), where c is the supergolden ratio A092526.
%H A382641 Wikipedia, <a href="https://en.wikipedia.org/wiki/Supergolden_ratio">Supergolden ratio</a>
%H A382641 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1).
%F A382641 G.f.: (1 + x^2 + x^4 - x^8)/(1 - x - x^3).
%F A382641 a(n) = a(n-1) + a(n-3) for n>=9.
%F A382641 a(n) = round(((2/3)*cos((1/3)*arccos(29/2))+1/3)^n) = round(A092526^n).
%F A382641 a(n) = A001609(n) for n>=6.
%t A382641 r = Root[x^3-x^2-1, 1]; Table[Round[r^i], {i,0,120 }]
%t A382641 CoefficientList[Series[(1+x^2+x^4-x^8)/(1-x-x^3), {x,0,120}], x]
%Y A382641 Cf. A000930, A001609, A092526, A169985, A205579.
%K A382641 nonn,easy
%O A382641 0,3
%A A382641 _Jwalin Bhatt_, Apr 01 2025