A325110 - OEIS

%I #9 Dec 12 2020 19:05:51

%S 1,1,1,2,1,2,2,5,2,3,2,6,3,6,7,15,8,10,6,13,6,10,12,23,13,16,16,26,21,

%T 30,37,60,43,52,42,60,42,50,54,81,59,60,66,80,74,86,108,145,119,125,

%U 126,144,134,140,170,208,189,193,221,248,253,292,323,435,392

%N Number of strict integer partitions of n with no binary containments.

%C A pair of positive integers is a binary containment if the positions of 1's in the reversed binary expansion of the first are a subset of the positions of 1's in the reversed binary expansion of the second.

%H Fausto A. C. Cariboni, <a href="/A325110/b325110.txt">Table of n, a(n) for n = 0..600</a>

%e The a(1) = 1 through a(12) = 3 partitions (A = 10, B = 11, C = 12):

%e   (1)  (2)  (3)   (4)  (5)   (6)   (7)    (8)   (9)   (A)   (B)    (C)

%e             (21)       (41)  (42)  (43)   (53)  (63)  (82)  (65)   (84)

%e                                    (52)         (81)        (83)   (93)

%e                                    (61)                     (92)

%e                                    (421)                    (A1)

%e                                                             (821)

%t binpos[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];

%t stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];

%t Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&stableQ[#,SubsetQ[binpos[#1],binpos[#2]]&]&]],{n,0,30}]

%Y Cf. A019565, A050315, A267610, A267700.

%Y Cf. A325101, A325106, A325107, A325108, A325109, A325119.

%K nonn

%O 0,4

%A _Gus Wiseman_, Mar 28 2019