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 A381079 #7 Mar 06 2025 22:13:37
%S A381079 0,1,0,0,1,1,0,3,1,3,1,2,0,7,2,6,7,11,3,19,8,22,16,32,17,48,21,50,39,
%T A381079 71,35,101,58,120,89,156,97,228,133,267,203,352,228,483,322,571,444,
%U A381079 734,524,989,683,1160,942,1490,1103,1919,1438,2302,1890,2881,2243,3683,2842,4384,3703,5461
%N A381079 Number of integer partitions of n whose greatest multiplicity is equal to their sum of distinct parts.
%C A381079 Are there only 4 zeros?
%e A381079 The partition (3,2,2,1,1,1,1,1,1) has greatest multiplicity 6 and distinct parts (3,2,1) with sum 6, so is counted under a(13).
%e A381079 The a(1) = 1 through a(13) = 7 partitions:
%e A381079 1 . . 22 2111 . 2221 22211 333 331111 5111111 . 33331
%e A381079 22111 222111 32111111 322222
%e A381079 31111 411111 3331111
%e A381079 4411111
%e A381079 61111111
%e A381079 322111111
%e A381079 421111111
%t A381079 Table[Length[Select[IntegerPartitions[n],Max@@Length/@Split[#]==Total[Union[#]]&]],{n,0,30}]
%Y A381079 For greatest part instead of multiplicity we have A000005.
%Y A381079 Counting partitions by the LHS gives A091602, rank statistic A051903.
%Y A381079 Counting partitions by the RHS gives A116861, rank statistic A066328.
%Y A381079 These partitions are ranked by A381632, for part instead of multiplicity A246655.
%Y A381079 A000041 counts integer partitions, strict A000009.
%Y A381079 A008284 counts partitions by length, strict A008289.
%Y A381079 A047993 counts balanced partitions, ranks A106529.
%Y A381079 A091605 counts partitions with greatest multiplicity 2.
%Y A381079 A240312 counts partitions with max part = max multiplicity, ranks A381542.
%Y A381079 Cf. A027193, A047966, A048767, A051904, A212166, A237984, A239455, A241131, A362608, A363724.
%K A381079 nonn
%O A381079 0,8
%A A381079 _Gus Wiseman_, Mar 03 2025