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 A239497 #12 Jan 28 2022 00:59:13
%S A239497 0,0,1,1,2,3,4,5,7,9,11,15,17,22,28,34,40,52,60,75,90,109,129,160,186,
%T A239497 225,268,321,376,455,530,632,743,878,1028,1219,1416,1667,1947,2281,
%U A239497 2648,3103,3593,4189,4857,5638,6516,7564,8715,10080,11614,13394,15392
%N A239497 Number of partitions p of n such that if h = min(p), then h is an (h,1)-separator of p; see Comments.
%C A239497 Suppose that p is a partition of n into 2 or more parts and that h is a part of p. Then p is (h,0)-separable if there is an ordering x, h, x, h, ..., h, x of the parts of p, where each x represents any part of p except h. Here, the number of h's on the ends of the ordering is 0. Similarly, p is (h,1)-separable if there is an ordering x, h, x, h, ..., x, h, where the number of h's on the ends is 1; next, p is (h,2)-separable if there is an ordering h, x, h, ..., x, h. Finally, p is h-separable if it is (h,i)-separable for i = 0,1,2.
%e A239497 a(7) counts these partitions: 61, 52, 43, 3211.
%t A239497 z = 35; t1 = Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, Min[p]] == Length[p]], {n, 1, z}] (* A239497 *)
%t A239497 t2 = Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, 2 Min[p]] == Length[p]], {n, 1, z}] (* A239498 *)
%t A239497 t3 = Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, Max[p]] == Length[p]], {n, 1, z}] (* A118096 *)
%t A239497 t4 = Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, Length[p]] == Length[p]], {n, 1, z}] (* A239500 *)
%t A239497 t5 = Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, Max[p] - Min[p]] == Length[p]], {n, 1, z}] (* A239501 *)
%Y A239497 Cf. A239498, A118096, A239500, A239501, A239482.
%K A239497 nonn,easy
%O A239497 1,5
%A A239497 _Clark Kimberling_, Mar 24 2014