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 A254685 #38 Sep 08 2022 08:46:11
%S A254685 1,1,2,4,7,12,22,39,69,123,219,389,692,1231,2189,3893,6924,12314,
%T A254685 21900,38949,69270,123195,219100,389665,693011,1232506,2191987,
%U A254685 3898404,6933232,12330612,21929742,39001599,69363549,123361658,219396194,390191659,693947912
%N A254685 Number of partially ordered partitions of n into parts less than or equal to 3, in which the order of adjacent 2's and 3's is unimportant.
%C A254685 Also number of compositions of n into parts 1, 2, 3, and 5.
%H A254685 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,0,-1).
%F A254685 G.f.: 1/(x^5 - x^3 - x^2 - x + 1).
%F A254685 a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-5).
%e A254685 a(7)=39. These are (331),(313),(133),(322=232=223),(3211=2311),(1123=1132),(1231=1321),(3112),(2113),(1312),(1213),(3121),(2131),(31111),(13111),(11311),(11131),(11113),(2221),(2212),(2122),(1222),(22111),(21211),(12211),(12121),(11221),(11212),(11122),(12112),(21112),(21121),(211111),(121111),(112111),(111211),(111121),(111112),(1111111).
%t A254685 CoefficientList[Series[1/(x^5 - x^3 - x^2 - x + 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, May 06 2015 *)
%o A254685 (Magma) I:=[1,2,4,7,12]; [n le 5 select I[n] else Self(n-1)+Self(n-2)+Self(n-3)-Self(n-5): n in [1..40]]; // _Vincenzo Librandi_, May 06 2015
%Y A254685 Cf. A001399.
%K A254685 nonn,easy
%O A254685 0,3
%A A254685 _David Neil McGrath_, May 04 2015
%E A254685 Corrected g.f. and more terms from _Vincenzo Librandi_, May 06 2015
%E A254685 a(0) added and g.f. adapted from _Alois P. Heinz_, May 08 2015