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 A239195 #23 Jul 08 2025 00:39:08
%S A239195 1,5,17,42,78,134,215,315,447,616,812,1052,1341,1665,2045,2486,2970,
%T A239195 3522,4147,4823,5579,6420,7320,8312,9401,10557,11817,13186,14630,
%U A239195 16190,17871,19635,21527,23552,25668,27924,30325,32825,35477,38286,41202,44282,47531
%N A239195 Sum of the next to smallest parts in the partitions of 4n into 4 parts with smallest part = 1.
%H A239195 Vincenzo Librandi, <a href="/A239195/b239195.txt">Table of n, a(n) for n = 1..1000</a>
%H A239195 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H A239195 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,2,-4,2,-1,2,-1).
%F A239195 G.f.: x*(4*x^5+5*x^4+11*x^3+8*x^2+3*x+1) / ((x-1)^4*(x^2+x+1)^2). - _Colin Barker_, Mar 12 2014
%F A239195 a(n) = 2*a(n-1)-a(n-2)+2*a(n-3)-4*a(n-4)+2*a(n-5)-a(n-6)+2*a(n-7)-a(n-8). - _Wesley Ivan Hurt_, Jul 08 2025
%e A239195 For a(n) add the numbers in the third columns.
%e A239195 13+ 1 + 1 + 1
%e A239195 12+ 2 + 1 + 1
%e A239195 11+ 3 + 1 + 1
%e A239195 10+ 4 + 1 + 1
%e A239195 9 + 5 + 1 + 1
%e A239195 8 + 6 + 1 + 1
%e A239195 7 + 7 + 1 + 1
%e A239195 11+ 2 + 2 + 1
%e A239195 10+ 3 + 2 + 1
%e A239195 9 + 1 + 1 + 1 9 + 4 + 2 + 1
%e A239195 8 + 2 + 1 + 1 8 + 5 + 2 + 1
%e A239195 7 + 3 + 1 + 1 7 + 6 + 2 + 1
%e A239195 6 + 4 + 1 + 1 9 + 3 + 3 + 1
%e A239195 5 + 5 + 1 + 1 8 + 4 + 3 + 1
%e A239195 7 + 2 + 2 + 1 7 + 5 + 3 + 1
%e A239195 5 + 1 + 1 + 1 6 + 3 + 2 + 1 6 + 6 + 3 + 1
%e A239195 4 + 2 + 1 + 1 5 + 4 + 2 + 1 7 + 4 + 4 + 1
%e A239195 3 + 3 + 1 + 1 5 + 3 + 3 + 1 6 + 5 + 4 + 1
%e A239195 1 + 1 + 1 + 1 3 + 2 + 2 + 1 4 + 4 + 3 + 1 5 + 5 + 5 + 1
%e A239195 4(1) 4(2) 4(3) 4(4) .. 4n
%e A239195 ------------------------------------------------------------------------
%e A239195 1 5 17 42 .. a(n)
%t A239195 b[n_] := Sum[(((4 n - 2 - i)*Floor[(4 n - 2 - i)/2] - i (4 n - 2 - i) + (i + 2) (Floor[(4 n - 2 - i)/2] - i)) - ((4 n - 2 - i)*Floor[(4 n - 2 - i)/2] - i (4 n - 2 - i)) - ((4 n - 2 - i)*Floor[(4 n - 2 - i)/2] - i (4 n - 2 - i) + (i + 2) (Floor[(4 n - 2 - i)/2] - i))/(4 n)) (Floor[(Sign[(Floor[(4 n - 2 - i)/2] - i)] + 2)/2]), {i, 0, 2 n}]; Table[b[n], {n, 50}]
%t A239195 LinearRecurrence[{2,-1,2,-4,2,-1,2,-1},{1,5,17,42,78,134,215,315},60] (* _Harvey P. Dale_, Jul 05 2025 *)
%o A239195 (PARI) Vec(x*(4*x^5+5*x^4+11*x^3+8*x^2+3*x+1)/((x-1)^4*(x^2+x+1)^2) + O(x^100)) \\ _Colin Barker_, Sep 22 2014
%Y A239195 Cf. A238328, A238340, A238702, A238705, A238706, A239056, A239057, A239059, A239186.
%K A239195 nonn,easy
%O A239195 1,2
%A A239195 _Wesley Ivan Hurt_, Mar 11 2014