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 A238705 #36 Dec 29 2021 15:21:54
%S A238705 1,4,10,19,30,44,61,80,102,127,154,184,217,252,290,331,374,420,469,
%T A238705 520,574,631,690,752,817,884,954,1027,1102,1180,1261,1344,1430,1519,
%U A238705 1610,1704,1801,1900,2002,2107,2214,2324,2437,2552,2670,2791,2914,3040,3169
%N A238705 Number of partitions of 4n into 4 parts with smallest part = 1.
%C A238705 The number of partitions of 4*(n-1) into at most 3 parts. - _Colin Barker_, Mar 31 2015
%H A238705 Vincenzo Librandi, <a href="/A238705/b238705.txt">Table of n, a(n) for n = 1..200</a>
%H A238705 A. Osorio, <a href="http://mpra.ub.uni-muenchen.de/56690/1/MPRA_paper_56690.pdf">A Sequential Allocation Problem: The Asymptotic Distribution of Resources</a>, Munich Personal RePEc Archive, 2014.
%H A238705 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A238705 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1).
%F A238705 G.f.: -x*(x+1)*(2*x^2+x+1) / ((x-1)^3*(x^2+x+1)). - _Colin Barker_, Mar 10 2014
%F A238705 a(n) = 2*a(n-1)-a(n-2)+a(n-3)-2*a(n-4)+a(n-5). - _Wesley Ivan Hurt_, Nov 18 2021
%e A238705 Count the 1's in the last column for a(n):
%e A238705 13 + 1 + 1 + 1
%e A238705 12 + 2 + 1 + 1
%e A238705 11 + 3 + 1 + 1
%e A238705 10 + 4 + 1 + 1
%e A238705 9 + 5 + 1 + 1
%e A238705 8 + 6 + 1 + 1
%e A238705 7 + 7 + 1 + 1
%e A238705 11 + 2 + 2 + 1
%e A238705 10 + 3 + 2 + 1
%e A238705 9 + 4 + 2 + 1
%e A238705 8 + 5 + 2 + 1
%e A238705 7 + 6 + 2 + 1
%e A238705 9 + 3 + 3 + 1
%e A238705 8 + 4 + 3 + 1
%e A238705 7 + 5 + 3 + 1
%e A238705 6 + 6 + 3 + 1
%e A238705 7 + 4 + 4 + 1
%e A238705 6 + 5 + 4 + 1
%e A238705 5 + 5 + 5 + 1
%e A238705 9 + 1 + 1 + 1 10 + 2 + 2 + 2
%e A238705 8 + 2 + 1 + 1 9 + 3 + 2 + 2
%e A238705 7 + 3 + 1 + 1 8 + 4 + 2 + 2
%e A238705 6 + 4 + 1 + 1 7 + 5 + 2 + 2
%e A238705 5 + 5 + 1 + 1 6 + 6 + 2 + 2
%e A238705 7 + 2 + 2 + 1 8 + 3 + 3 + 2
%e A238705 6 + 3 + 2 + 1 7 + 4 + 3 + 2
%e A238705 5 + 4 + 2 + 1 6 + 5 + 3 + 2
%e A238705 5 + 3 + 3 + 1 6 + 4 + 4 + 2
%e A238705 4 + 4 + 3 + 1 5 + 5 + 4 + 2
%e A238705 5 + 1 + 1 + 1 6 + 2 + 2 + 2 7 + 3 + 3 + 3
%e A238705 4 + 2 + 1 + 1 5 + 3 + 2 + 2 6 + 4 + 3 + 3
%e A238705 3 + 3 + 1 + 1 4 + 4 + 2 + 2 5 + 5 + 3 + 3
%e A238705 3 + 2 + 2 + 1 4 + 3 + 3 + 2 5 + 4 + 4 + 3
%e A238705 1 + 1 + 1 + 1 2 + 2 + 2 + 2 3 + 3 + 3 + 3 4 + 4 + 4 + 4
%e A238705 4(1) 4(2) 4(3) 4(4) .. 4n
%e A238705 ------------------------------------------------------------------------
%e A238705 1 4 10 19 .. a(n)
%t A238705 a[1] = 4; a[n_] := (n/(n - 1))*a[n - 1] + 4 n*Sum[(Floor[(4 n - 2 - i)/2] - i)*(Floor[(Sign[(Floor[(4 n - 2 - i)/2] - i)] + 2)/2]), {i, 0, 2 n}]; b[n_] := a[n]/(4 n); Table[b[n] - b[n - 1], {n, 50}]
%t A238705 LinearRecurrence[{2,-1,1,-2,1},{1,4,10,19,30},50] (* _Harvey P. Dale_, Jun 13 2015 *)
%t A238705 Table[Count[IntegerPartitions[4 n,{4}],_?(#[[-1]]==1&)],{n,50}] (* _Harvey P. Dale_, Dec 29 2021 *)
%o A238705 (PARI) Vec(-x*(x+1)*(2*x^2+x+1)/((x-1)^3*(x^2+x+1)) + O(x^100)) \\ _Colin Barker_, Sep 22 2014
%Y A238705 Cf. A238328, A238340, A238702.
%K A238705 nonn,easy
%O A238705 1,2
%A A238705 _Wesley Ivan Hurt_ and _Antonio Osorio_, Mar 03 2014