cp's OEIS Frontend

A350844 Number of strict integer partitions of n with no difference -2.

%I A350844 #9 Jan 25 2022 10:26:18
%S A350844 1,1,1,2,1,3,3,4,4,7,7,8,11,12,15,18,21,23,31,32,40,45,54,59,73,78,94,
%T A350844 106,122,136,161,177,203,231,259,293,334,372,417,476,525,592,663,742,
%U A350844 821,931,1020,1147,1271,1416,1558,1752,1916,2137,2357,2613,2867
%N A350844 Number of strict integer partitions of n with no difference -2.
%H A350844 Gus Wiseman, <a href="/A069916/a069916.txt">Sequences counting and ranking partitions and compositions by their differences and quotients</a>.
%e A350844 The a(1) = 1 through a(12) = 11 partitions (A..C = 10..12):
%e A350844   1   2   3    4   5    6     7    8     9     A      B     C
%e A350844           21       32   51    43   62    54    73     65    84
%e A350844                    41   321   52   71    63    82     74    93
%e A350844                               61   521   72    91     83    A2
%e A350844                                          81    541    92    B1
%e A350844                                          432   721    A1    543
%e A350844                                          621   4321   632   651
%e A350844                                                       821   732
%e A350844                                                             741
%e A350844                                                             921
%e A350844                                                             6321
%t A350844 Table[Length[Select[IntegerPartitions[n],FreeQ[Differences[#],0|-2]&]],{n,0,30}]
%Y A350844 The version for no difference 0 is A000009.
%Y A350844 The version for no difference > -2 is A001227, non-strict A034296.
%Y A350844 The version for no difference -1 is A003114 (A325160).
%Y A350844 The version for subsets of prescribed maximum is A005314.
%Y A350844 The version for all differences < -2 is A025157, non-strict A116932.
%Y A350844 The opposite version is A072670.
%Y A350844 The multiplicative version is A350840, non-strict A350837 (A350838).
%Y A350844 The non-strict version is A350842.
%Y A350844 A000041 counts integer partitions.
%Y A350844 A027187 counts partitions of even length.
%Y A350844 A027193 counts partitions of odd length (A026424).
%Y A350844 A116931 counts partitions with no difference -1 (A319630).
%Y A350844 A323092 counts double-free integer partitions (A320340) strict A120641.
%Y A350844 A325534 counts separable partitions (A335433).
%Y A350844 A325535 counts inseparable partitions (A335448).
%Y A350844 Cf. A000929, A003000, A018819, A040039, A045690, A045691, A154402, A303362, A323094, A342095, A342097.
%K A350844 nonn
%O A350844 0,4
%A A350844 _Gus Wiseman_, Jan 21 2022