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 A120400 #36 Mar 20 2022 14:10:52
%S A120400 1,1,2,3,5,8,14,23,39,65,109,182,305,510,854,1429,2392,4003,6700,
%T A120400 11213,18767,31409,52568,87980,147248,246441,412456,690306,1155330,
%U A120400 1933616,3236194,5416251,9064901,15171458,25391689,42496763,71124646,119037660
%N A120400 Expansion of 1/(1-x-x^2-x^6).
%C A120400 Number of compositions of n into parts 1, 2, and 6. - _Joerg Arndt_, Sep 30 2012
%C A120400 Counts partitions of n into parts (1,2,3,4,5) where only the position (order) of the 4's and 5's are important. - _David Neil McGrath_, May 12 2015
%H A120400 Harvey P. Dale, <a href="/A120400/b120400.txt">Table of n, a(n) for n = 0..1000</a>
%H A120400 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,0,0,1).
%F A120400 G.f.: 1/(1-x-x^2-x^6).
%F A120400 a(n) = a(n-1) + a(n-2) + a(n-6).
%e A120400 Compositions of n into parts (1,2,6). a(6)=14 These are (6),(222),(2211),(1122),(1221),(2112),(2121),(1212),(21111),(12111),(11211),(11121),(11112),(111111). - _David Neil McGrath_, May 12 2015
%e A120400 Partial Partitions of n into parts (1,2,3,4,5) with only the position of 4's,5's important. a(8)=39; these are (53),(35),(521,512=one),(215,125=one),(251),(152),(5111),(1511),(1151),(1115),(44),(431,413=one),(314,134=one),(341),(143),(422),(224),(242),(4211,4121,4112=one),(2114,1214,1124=one),(2411),(1142),(2141,1241=one),(1421,1412=one),(41111),(14111),(11411),(11141),(11114),(332),(3311),(3221),(32111),(311111),(2222),(22211),(221111),(2111111),(11111111). - _David Neil McGrath_, May 12 2015
%t A120400 CoefficientList[Series[1/(1-x-x^2-x^6),{x,0,40}],x] (* or *) LinearRecurrence[{1,1,0,0,0,1},{1,1,2,3,5,8},40] (* _Harvey P. Dale_, Jun 19 2012 *)
%o A120400 (Magma) [n le 6 select Fibonacci(n) else Self(n-1)+Self(n-2)+Self(n-6): n in [1..40]]; // _Vincenzo Librandi_, May 12 2015
%o A120400 (Sage)
%o A120400 m = 40; L.<x> = PowerSeriesRing(ZZ, m)
%o A120400 f = 1/(1-x-x^2-x^6); print(f.coefficients())
%o A120400 # _Bruno Berselli_, May 12 2015
%K A120400 nonn,easy
%O A120400 0,3
%A A120400 _Jon E. Schoenfield_, Aug 27 2006