A342342 - OEIS

A342342

Number of strict compositions of n with all adjacent parts (x, y) satisfying x <= 2y and y <= 2x.

1, 1, 1, 3, 1, 3, 5, 5, 3, 11, 9, 11, 17, 15, 29, 39, 31, 39, 65, 57, 107, 127, 149, 155, 187, 265, 293, 419, 523, 571, 781, 763, 941, 1371, 1387, 2125, 2383, 2775, 3243, 4189, 4555, 5349, 7241, 7997, 10591, 13171, 14581, 17213, 20253, 25177, 27701, 34317

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OFFSET

0,4

COMMENTS

Each quotient of adjacent parts is between 1/2 and 2 inclusive.

LINKS

Table of n, a(n) for n=0..51.

EXAMPLE

The a(1) = 1 through a(12) = 17 strict compositions (A = 10, B = 11, C = 12):

1 2 3 4 5 6 7 8 9 A B C

12 23 24 34 35 36 46 47 48

21 32 42 43 53 45 64 56 57

123 124 54 235 65 75

321 421 63 532 74 84

234 1234 236 246

243 1243 245 345

324 3421 542 354

342 4321 632 435

423 1235 453

432 5321 534

543

642

1236

1245

5421

6321

MATHEMATICA

Table[Length[Select[Join@@Permutations/@Select[IntegerPartitions[n], UnsameQ@@#&], And@@Table[#[[i]]<=2*#[[i-1]]&&#[[i-1]]<=2*#[[i]], {i, 2, Length[#]}]&]], {n, 0, 15}]

CROSSREFS

The non-strict version is A224957.

The case with strict relations is A342341 (non-strict: A342330).

A000929 counts partitions with adjacent parts x >= 2y.

A002843 counts compositions with adjacent parts x <= 2y.

A154402 counts partitions with adjacent parts x = 2y.

A274199 counts compositions with adjacent parts x < 2y.

A342094 counts partitions with adjacent x <= 2y (strict: A342095).

A342096 counts partitions without adjacent x >= 2y (strict: A342097).

A342098 counts partitions with adjacent parts x > 2y.

A342331 counts compositions with adjacent parts x = 2y or y = 2x.

A342332 counts compositions with adjacent parts x > 2y or y > 2x.

A342333 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.

A342338 counts compositions with adjacent parts x < 2y and y <= 2x.

Cf. A003114, A003242, A034296, A167606, A342083, A342084, A342087, A342191, A342334, A342336, A342340.

Sequence in context: A082082 A016646 A345943 * A182600 A371928 A179760

Adjacent sequences: A342339 A342340 A342341 * A342343 A342344 A342345

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 12 2021

EXTENSIONS

a(40)-a(51) from Alois P. Heinz, May 24 2021

STATUS

approved