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 A003522 M1391 #46 Jan 05 2025 19:51:33
%S A003522 1,1,1,1,2,5,11,21,37,64,113,205,377,693,1266,2301,4175,7581,13785,
%T A003522 25088,45665,83097,151169,274969,500162,909845,1655187,3011157,
%U A003522 5477917,9965312,18128529,32978725,59993817,109139117,198543154
%N A003522 a(n) = Sum_{k=0..n} C(n-k,3k).
%D A003522 A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 113.
%D A003522 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003522 Seiichi Manyama, <a href="/A003522/b003522.txt">Table of n, a(n) for n = 0..3850</a>
%H A003522 V. C. Harris, C. C. Styles, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/2-4/harris.pdf">A generalization of Fibonacci numbers</a>, Fib. Quart. 2 (1964) 277-289, sequence u(n,1,3).
%H A003522 V. E. Hoggatt, Jr., <a href="/A005676/a005676.pdf">7-page typed letter to N. J. A. Sloane with suggestions for new sequences</a>, circa 1977.
%H A003522 Vedran Krcadinac, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/44-4/quartkrcadinac04_2006.pdf">A new generalization of the golden ratio</a>, Fibonacci Quart. 44 (2006), no. 4, 335-340.
%H A003522 Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H A003522 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H A003522 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1, 1).
%F A003522 G.f. : (1-x)^2/(1-3x+3x^2-x^3-x^4); a(n)=3a(n-1)-3a(n-2)+a(n-3)+a(n-4). - _Paul Barry_, Jul 07 2004
%p A003522 A003522:=-(z-1)**2/(-1+3*z-3*z**2+z**4+z**3); # conjectured by _Simon Plouffe_ in his 1992 dissertation
%t A003522 LinearRecurrence[{3, -3, 1, 1},{1, 1, 1, 1},35] (* _Ray Chandler_, Sep 23 2015 *)
%o A003522 (PARI) a(n)=if(n<0, 0, polcoeff((1-x)^2/(1-3*x+3*x^2-x^3-x^4)+x*O(x^n), n)) /* _Michael Somos_, Sep 20 2005 */
%K A003522 nonn,easy
%O A003522 0,5
%A A003522 _N. J. A. Sloane_