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 A360670 #7 Feb 19 2023 20:52:02
%S A360670 1,0,0,0,1,0,0,0,1,1,0,0,2,0,0,1,2,0,2,0,2,2,0,0,5,1,0,3,3,0,4,0,5,3,
%T A360670 0,2,10,0,0,4,10,0,5,0,7,9,0,0,17,1,6,5,10,0,9,8,14,6,0,0,34,0,0,9,18,
%U A360670 13,13,0,17,7,19,0,40,0,0,28
%N A360670 Number of integer partitions of n whose parts have the same mean as their negated first differences.
%e A360670 The a(n) partitions for n = 4, 12, 24, 27, 30, 44:
%e A360670 (3,1) (9,3) (18,6) (19,7,1) (21,8,1) (33,11)
%e A360670 (9,2,1) (17,6,1) (20,5,2) (22,6,2) (34,5,4,1)
%e A360670 (18,4,2) (21,3,3) (23,4,3) (34,6,3,1)
%e A360670 (19,2,2,1) (25,2,1,1,1) (34,7,2,1)
%e A360670 (19,3,1,1) (34,8,1,1)
%e A360670 (35,4,3,2)
%e A360670 (35,5,2,2)
%e A360670 For example, the partition y = (28,4,3,1), with mean 9, has negated first differences (24,2,1), with mean 9, so y is counted under a(36).
%t A360670 Table[Length[Select[IntegerPartitions[n], Mean[#]==Mean[Differences[Reverse[#]]]&]],{n,0,30}]
%Y A360670 These partitions have ranks A360669.
%Y A360670 A000041 counts integer partitions, strict A000009.
%Y A360670 A058398 counts partitions by mean, see also A008284, A327482.
%Y A360670 A067538 counts partitions with integer mean, strict A102627, ranks A316413.
%Y A360670 A326567/A326568 gives mean of prime indices.
%Y A360670 A360614/A360615 = mean of first differences of 0-prepended prime indices.
%Y A360670 Cf. A060016, A240219, A116608, A316313, A340610, A360068.
%K A360670 nonn
%O A360670 0,13
%A A360670 _Gus Wiseman_, Feb 18 2023