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 A332576 #7 Mar 05 2020 22:56:44
%S A332576 1,1,2,3,4,6,6,10,12,17,21,31,35,51,59,80,97,130,153,204,244,308,376,
%T A332576 475,564,708,851,1043,1247,1533,1816,2216,2633,3174,3766,4526,5324,
%U A332576 6376,7520,8917,10479,12415,14524,17134,20035,23489,27423,32091,37286,43512
%N A332576 Number of integer partitions of n that are all 1's or whose run-lengths cover an initial interval of positive integers.
%C A332576 First differs from A317491 at a(11) = 31, A317491(11) = 30.
%F A332576 a(n > 1) = A317081(n) + 1.
%e A332576 The a(1) = 1 through a(8) = 12 partitions:
%e A332576 (1) (2) (3) (4) (5) (6) (7) (8)
%e A332576 (11) (21) (31) (32) (42) (43) (53)
%e A332576 (111) (211) (41) (51) (52) (62)
%e A332576 (1111) (221) (321) (61) (71)
%e A332576 (311) (411) (322) (332)
%e A332576 (11111) (111111) (331) (422)
%e A332576 (421) (431)
%e A332576 (511) (521)
%e A332576 (3211) (611)
%e A332576 (1111111) (3221)
%e A332576 (4211)
%e A332576 (11111111)
%t A332576 nQ[ptn_]:=Or[ptn=={},Union[ptn]=={1},Union[Length/@Split[ptn]]==Range[Max[Length/@Split[ptn]]]];
%t A332576 Table[Length[Select[IntegerPartitions[n],nQ]],{n,0,30}]
%Y A332576 The narrow version is A317081.
%Y A332576 Heinz numbers of these partitions first differ from A317492 in having 420.
%Y A332576 Not counting constant-1 sequences gives A317081.
%Y A332576 Dominated by A332295.
%Y A332576 Cf. A000009, A001462, A181819, A182850, A317245, A317491, A329746, A329747, A332272, A332277.
%K A332576 nonn
%O A332576 0,3
%A A332576 _Gus Wiseman_, Mar 05 2020