A342334 Number of compositions of n with all adjacent parts (x, y) satisfying x >= 2y or y > 2x.
1, 1, 1, 2, 3, 4, 6, 11, 16, 23, 35, 54, 82, 125, 193, 294, 447, 680, 1037, 1580, 2408, 3676, 5606, 8544, 13024, 19860, 30277, 46155, 70374, 107300, 163586, 249397, 380235, 579705, 883810, 1347467, 2054371, 3132102, 4775211, 7280321, 11099613, 16922503, 25800136, 39335052, 59970425, 91431195
Offset: 0
Keywords
Examples
The a(1) = 1 through a(8) = 16 compositions: (1) (2) (3) (4) (5) (6) (7) (8) (12) (13) (14) (15) (16) (17) (31) (41) (24) (25) (26) (131) (51) (52) (62) (141) (61) (71) (312) (124) (125) (151) (152) (241) (161) (313) (251) (412) (314) (1312) (413) (512) (1241) (1313) (1412) (3131)
Crossrefs
The version not allowing equality (i.e., strict relations) is A342332.
The version allowing equality (i.e., non-strict relations) is A342333.
Reversing operators and changing 'or' into 'and' gives A342338.
A002843 counts compositions with adjacent parts x <= 2y.
A154402 counts partitions with adjacent parts x = 2y.
A274199 counts compositions with adjacent parts x < 2y.
A342331 counts compositions with adjacent parts x = 2y or y = 2x.
A342335 counts compositions with adjacent parts x >= 2y or y = 2x.
A342337 counts partitions with adjacent parts x = y or x = 2y.
Programs
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Mathematica
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],And@@Table[#[[i]]>=2*#[[i-1]]||#[[i-1]]>2*#[[i]],{i,2,Length[#]}]&]],{n,0,15}]
Extensions
More terms from Joerg Arndt, Mar 12 2021
Comments