A325110 Number of strict integer partitions of n with no binary containments.

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, 30, 37, 60, 43, 52, 42, 60, 42, 50, 54, 81, 59, 60, 66, 80, 74, 86, 108, 145, 119, 125, 126, 144, 134, 140, 170, 208, 189, 193, 221, 248, 253, 292, 323, 435, 392

Offset: 0

Author

Gus Wiseman, Mar 28 2019

Keywords

• nonn

Comments

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.

Examples

			The a(1) = 1 through a(12) = 3 partitions (A = 10, B = 11, C = 12):
  (1)  (2)  (3)   (4)  (5)   (6)   (7)    (8)   (9)   (A)   (B)    (C)
            (21)       (41)  (42)  (43)   (53)  (63)  (82)  (65)   (84)
                                   (52)         (81)        (83)   (93)
                                   (61)                     (92)
                                   (421)                    (A1)
                                                            (821)
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..600

Crossrefs

Cf. A019565, A050315, A267610, A267700.

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

Programs

Mathematica

binpos[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&stableQ[#,SubsetQ[binpos[#1],binpos[#2]]&]&]],{n,0,30}]