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 A342341 #10 Mar 20 2021 13:49:58
%S A342341 1,1,1,1,1,3,1,3,3,5,5,5,9,7,13,15,17,19,29,31,39,43,63,59,75,121,119,
%T A342341 169,167,199,279,305,343,479,537,733,789,883,1057,1421,1545,1831,2409,
%U A342341 2577,3343,4001,4657,5131,6065,7755,8841,10473,12995,14659,17671,20619,25157,28255,33131,38265,47699,53171,62611,80005,88519,105937,119989
%N A342341 Number of strict compositions of n with all adjacent parts (x, y) satisfying x < 2y and y < 2x.
%C A342341 Each quotient of adjacent parts is between 1/2 and 2 exclusive.
%H A342341 Bert Dobbelaere, <a href="/A342341/b342341.txt">Table of n, a(n) for n = 0..100</a>
%e A342341 The a(1) = 1 through a(17) = 17 compositions (A..G = 10..16):
%e A342341 1 2 3 4 5 6 7 8 9 A B C D E F G
%e A342341 23 34 35 45 46 47 57 58 59 69 6A
%e A342341 32 43 53 54 64 56 75 67 68 78 79
%e A342341 234 235 65 345 76 86 87 97
%e A342341 432 532 74 354 85 95 96 A6
%e A342341 435 346 347 357 358
%e A342341 453 643 356 456 457
%e A342341 534 653 465 475
%e A342341 543 743 546 547
%e A342341 2345 564 574
%e A342341 2354 645 745
%e A342341 4532 654 754
%e A342341 5432 753 853
%e A342341 2346 2347
%e A342341 6432 2356
%e A342341 6532
%e A342341 7432
%t A342341 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 A342341 The unordered version (partitions) is A342097 (non-strict: A342096).
%Y A342341 The non-strict version is A342330.
%Y A342341 The version allowing equality is A342342 (non-strict: A224957).
%Y A342341 A000929 counts partitions with adjacent parts x >= 2y.
%Y A342341 A002843 counts compositions with adjacent parts x <= 2y.
%Y A342341 A154402 counts partitions with adjacent parts x = 2y.
%Y A342341 A274199 counts compositions with adjacent parts x < 2y.
%Y A342341 A342094 counts partitions with adjacent x <= 2y (strict: A342095).
%Y A342341 A342098 counts partitions with adjacent parts x > 2y.
%Y A342341 A342331 counts compositions with adjacent parts x = 2y or y = 2x.
%Y A342341 A342332 counts compositions with adjacent parts x > 2y or y > 2x.
%Y A342341 A342333 counts compositions with adjacent parts x >= 2y or y >= 2x.
%Y A342341 A342335 counts compositions with adjacent parts x >= 2y or y = 2x.
%Y A342341 A342337 counts partitions with adjacent parts x = y or x = 2y.
%Y A342341 A342338 counts compositions with adjacent parts x < 2y and y <= 2x.
%Y A342341 Cf. A003114, A003242, A034296, A167606, A342083, A342084, A342087, A342191, A342334, A342336, A342339, A342340.
%K A342341 nonn
%O A342341 0,6
%A A342341 _Gus Wiseman_, Mar 12 2021
%E A342341 More terms from _Bert Dobbelaere_, Mar 19 2021