cp's OEIS Frontend

A342334 Number of compositions of n with all adjacent parts (x, y) satisfying x >= 2y or y > 2x.

%I A342334 #14 Mar 12 2021 04:03:35
%S A342334 1,1,1,2,3,4,6,11,16,23,35,54,82,125,193,294,447,680,1037,1580,2408,
%T A342334 3676,5606,8544,13024,19860,30277,46155,70374,107300,163586,249397,
%U A342334 380235,579705,883810,1347467,2054371,3132102,4775211,7280321,11099613,16922503,25800136,39335052,59970425,91431195
%N A342334 Number of compositions of n with all adjacent parts (x, y) satisfying x >= 2y or y > 2x.
%C A342334 Also the number of compositions of n with all adjacent parts (x, y) satisfying x > 2y or y >= 2x.
%e A342334 The a(1) = 1 through a(8) = 16 compositions:
%e A342334   (1)  (2)  (3)   (4)   (5)    (6)    (7)     (8)
%e A342334             (12)  (13)  (14)   (15)   (16)    (17)
%e A342334                   (31)  (41)   (24)   (25)    (26)
%e A342334                         (131)  (51)   (52)    (62)
%e A342334                                (141)  (61)    (71)
%e A342334                                (312)  (124)   (125)
%e A342334                                       (151)   (152)
%e A342334                                       (241)   (161)
%e A342334                                       (313)   (251)
%e A342334                                       (412)   (314)
%e A342334                                       (1312)  (413)
%e A342334                                               (512)
%e A342334                                               (1241)
%e A342334                                               (1313)
%e A342334                                               (1412)
%e A342334                                               (3131)
%t A342334 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],And@@Table[#[[i]]>=2*#[[i-1]]||#[[i-1]]>2*#[[i]],{i,2,Length[#]}]&]],{n,0,15}]
%Y A342334 The unordered version (partitions) is A342098 or A000929 (multisets).
%Y A342334 The version not allowing equality (i.e., strict relations) is A342332.
%Y A342334 The version allowing equality (i.e., non-strict relations) is A342333.
%Y A342334 Reversing operators and changing 'or' into 'and' gives A342338.
%Y A342334 A002843 counts compositions with adjacent parts x <= 2y.
%Y A342334 A154402 counts partitions with adjacent parts x = 2y.
%Y A342334 A224957 counts compositions with x <= 2y and y <= 2x (strict: A342342).
%Y A342334 A274199 counts compositions with adjacent parts x < 2y.
%Y A342334 A342094 counts partitions with adjacent parts x <= 2y (strict: A342095).
%Y A342334 A342096 counts partitions without adjacent x >= 2y (strict: A342097).
%Y A342334 A342330 counts compositions with x < 2y and y < 2x (strict: A342341).
%Y A342334 A342331 counts compositions with adjacent parts x = 2y or y = 2x.
%Y A342334 A342335 counts compositions with adjacent parts x >= 2y or y = 2x.
%Y A342334 A342337 counts partitions with adjacent parts x = y or x = 2y.
%Y A342334 Cf. A003114, A003242, A034296, A167606, A342083, A342084, A342087, A342191, A342336, A342340.
%K A342334 nonn
%O A342334 0,4
%A A342334 _Gus Wiseman_, Mar 10 2021
%E A342334 More terms from _Joerg Arndt_, Mar 12 2021