cp's OEIS Frontend

A360254 Number of integer partitions of n with more adjacent equal parts than distinct parts.

%I A360254 #9 Feb 21 2023 07:34:04
%S A360254 0,0,0,1,1,1,3,4,7,10,12,18,28,36,52,68,92,119,161,204,269,355,452,
%T A360254 571,738,921,1167,1457,1829,2270,2834,3483,4314,5300,6502,7932,9665,
%U A360254 11735,14263,17227,20807,25042,30137,36099,43264,51646,61608,73291,87146,103296
%N A360254 Number of integer partitions of n with more adjacent equal parts than distinct parts.
%C A360254 None of these partitions is strict.
%C A360254 Also the number of integer partitions of n which, after appending 0, have first differences of median 0.
%e A360254 The a(3) = 1 through a(9) = 10 partitions:
%e A360254   (111)  (1111)  (11111)  (222)     (22111)    (2222)      (333)
%e A360254                           (21111)   (31111)    (22211)     (22221)
%e A360254                           (111111)  (211111)   (41111)     (33111)
%e A360254                                     (1111111)  (221111)    (51111)
%e A360254                                                (311111)    (222111)
%e A360254                                                (2111111)   (411111)
%e A360254                                                (11111111)  (2211111)
%e A360254                                                            (3111111)
%e A360254                                                            (21111111)
%e A360254                                                            (111111111)
%e A360254 For example, the partition y = (4,4,3,1,1,1,1) has 0-appended differences (0,1,2,0,0,0,0), with median 0, so y is counted under a(15).
%t A360254 Table[Length[Select[IntegerPartitions[n], Length[#]>2*Length[Union[#]]&]],{n,0,30}]
%Y A360254 The non-prepended version is A237363.
%Y A360254 These partitions have ranks A360558.
%Y A360254 For any integer median (not just 0) we have A360688.
%Y A360254 A000041 counts integer partitions, strict A000009.
%Y A360254 A008284 counts partitions by number of parts.
%Y A360254 A116608 counts partitions by number of distinct parts.
%Y A360254 A325347 counts partitions w/ integer median, strict A359907, ranks A359908.
%Y A360254 A359893 and A359901 count partitions by median, odd-length A359902.
%Y A360254 Cf. A000975, A027193, A067538, A102627, A240219, A359894, A360071, A360244, A360555, A360556.
%K A360254 nonn
%O A360254 0,7
%A A360254 _Gus Wiseman_, Feb 20 2023