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 A251655 #30 Mar 28 2025 10:09:53
%S A251655 0,1,1,1,3,6,11,21,41,79,152,293,565,1089,2099,4046,7799,15033,28977,
%T A251655 55855,107664,207529,400025,771073,1486291,2864918,5522307,10644589,
%U A251655 20518105,39549919,76234920,146947533,283250477,545982849,1052415779,2028596638
%N A251655 4-step Fibonacci sequence starting with 0, 1, 1, 1.
%H A251655 Tamás Lengyel and Diego Marques, <a href="https://www.emis.de/journals/INTEGERS/papers/r5/r5.Abstract.html">The 2-adic Order of Some Generalized Fibonacci Numbers</a>, INTEGERS, 17, 2017, A5.
%H A251655 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1).
%F A251655 a(n+4) = a(n) + a(n+1) + a(n+2) + a(n+3).
%F A251655 G.f.: x*(x-1)*(1+x)/(-1+x+x^2+x^3+x^4) . - _R. J. Mathar_, Mar 28 2025
%F A251655 a(n) = A000078(n+2)-A000078(n). - _R. J. Mathar_, Mar 28 2025
%t A251655 LinearRecurrence[Table[1, {4}], {0, 1, 1, 1}, 36] (* _Michael De Vlieger_, Dec 09 2014 *)
%o A251655 (J) (see www.jsoftware.com) First construct the generating matrix
%o A251655 [M=: (#.@}: + {:)\"1&.|: <:/~i.4
%o A251655 1 1 1 1
%o A251655 1 2 2 2
%o A251655 2 3 4 4
%o A251655 4 6 7 8
%o A251655 Given that matrix, one can produce the first 4*250 numbers with
%o A251655 , M(+/ . *)^:(i.250) 0 1 1 1x
%Y A251655 Other 4-step Fibonacci sequences are A000078, A000288, A001630, A001631, A001648, A073817, A100532, A251654, A251656, A251672, A251703, A251704, A251705.
%K A251655 nonn,easy
%O A251655 0,5
%A A251655 _Arie Bos_, Dec 06 2014