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 A361392 #6 Mar 19 2023 15:31:40
%S A361392 0,0,0,1,0,2,1,3,2,5,4,8,7,12,12,19,19,29,31,43,48,65,73,97,110,142,
%T A361392 164,208,240,301,350,432,504,617,719,874,1019,1228,1434,1717,2001,
%U A361392 2385,2778,3292,3831,4522,5252,6177,7164,8392,9722,11352,13125,15283,17643
%N A361392 Number of integer partitions of n whose first differences have mean -1.
%C A361392 These are partitions where the first part minus the last part is the number of parts minus 1.
%e A361392 The a(3) = 1 through a(11) = 8 partitions:
%e A361392 (21) . (32) (321) (43) (422) (54) (442) (65)
%e A361392 (311) (331) (4211) (432) (4321) (533)
%e A361392 (4111) (4221) (4411) (4331)
%e A361392 (4311) (52111) (4421)
%e A361392 (51111) (5222)
%e A361392 (52211)
%e A361392 (53111)
%e A361392 (611111)
%e A361392 For example, the partition y = (4,2,2,1) has first differences (-2,0,-1), with mean -1, so y is counted under a(9).
%t A361392 Table[Length[Select[IntegerPartitions[n],Mean[Differences[#]]==-1&]],{n,0,30}]
%Y A361392 For mean 0 we have A032741.
%Y A361392 The 0-appended version is A047993.
%Y A361392 For any negative mean we have A144300.
%Y A361392 A000041 counts integer partitions, strict A000009.
%Y A361392 A008284/A058398/A327482 count partitions by mean.
%Y A361392 A067538 counts partitions with integer mean, ranks A316413.
%Y A361392 A326567/A326568 gives mean of prime indices, conjugate A326839/A326840.
%Y A361392 A360614/A360615 gives mean of 0-appended first differences of prime indices.
%Y A361392 Cf. A102627, A237363, A237832, A348551, A360688.
%K A361392 nonn
%O A361392 0,6
%A A361392 _Gus Wiseman_, Mar 13 2023