This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A342342 #8 May 24 2021 06:41:42
%S A342342 1,1,1,3,1,3,5,5,3,11,9,11,17,15,29,39,31,39,65,57,107,127,149,155,
%T A342342 187,265,293,419,523,571,781,763,941,1371,1387,2125,2383,2775,3243,
%U A342342 4189,4555,5349,7241,7997,10591,13171,14581,17213,20253,25177,27701,34317
%N A342342 Number of strict compositions of n with all adjacent parts (x, y) satisfying x <= 2y and y <= 2x.
%C A342342 Each quotient of adjacent parts is between 1/2 and 2 inclusive.
%e A342342 The a(1) = 1 through a(12) = 17 strict compositions (A = 10, B = 11, C = 12):
%e A342342 1 2 3 4 5 6 7 8 9 A B C
%e A342342 12 23 24 34 35 36 46 47 48
%e A342342 21 32 42 43 53 45 64 56 57
%e A342342 123 124 54 235 65 75
%e A342342 321 421 63 532 74 84
%e A342342 234 1234 236 246
%e A342342 243 1243 245 345
%e A342342 324 3421 542 354
%e A342342 342 4321 632 435
%e A342342 423 1235 453
%e A342342 432 5321 534
%e A342342 543
%e A342342 642
%e A342342 1236
%e A342342 1245
%e A342342 5421
%e A342342 6321
%t A342342 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}]
%Y A342342 The non-strict version is A224957.
%Y A342342 The case with strict relations is A342341 (non-strict: A342330).
%Y A342342 A000929 counts partitions with adjacent parts x >= 2y.
%Y A342342 A002843 counts compositions with adjacent parts x <= 2y.
%Y A342342 A154402 counts partitions with adjacent parts x = 2y.
%Y A342342 A274199 counts compositions with adjacent parts x < 2y.
%Y A342342 A342094 counts partitions with adjacent x <= 2y (strict: A342095).
%Y A342342 A342096 counts partitions without adjacent x >= 2y (strict: A342097).
%Y A342342 A342098 counts partitions with adjacent parts x > 2y.
%Y A342342 A342331 counts compositions with adjacent parts x = 2y or y = 2x.
%Y A342342 A342332 counts compositions with adjacent parts x > 2y or y > 2x.
%Y A342342 A342333 counts compositions with adjacent parts x >= 2y or y >= 2x.
%Y A342342 A342335 counts compositions with adjacent parts x >= 2y or y = 2x.
%Y A342342 A342337 counts partitions with adjacent parts x = y or x = 2y.
%Y A342342 A342338 counts compositions with adjacent parts x < 2y and y <= 2x.
%Y A342342 Cf. A003114, A003242, A034296, A167606, A342083, A342084, A342087, A342191, A342334, A342336, A342340.
%K A342342 nonn
%O A342342 0,4
%A A342342 _Gus Wiseman_, Mar 12 2021
%E A342342 a(40)-a(51) from _Alois P. Heinz_, May 24 2021