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 A325849 #5 Jun 02 2019 00:48:39
%S A325849 1,1,1,3,3,5,9,13,19,23,51,57,91,117,179,283,381,531,737,1017,1335,
%T A325849 2259,2745,3983,5289,7367,9413,13155,19461,25129,33997,45633,61225,
%U A325849 80481,107091,137475,205243,253997,345527,447003,604919,768331,1026167,1299227
%N A325849 Number of strict compositions of n with no three consecutive parts in arithmetic progression.
%C A325849 A composition of n is a finite sequence of positive integers with sum n. a(n) is the number of strict compositions of n with no two of their adjacent first-differences equal, or with no 0's in their second-differences.
%H A325849 Wikipedia, <a href="https://en.wikipedia.org/wiki/Arithmetic_progression">Arithmetic progression</a>
%e A325849 The a(1) = 1 through a(8) = 19 compositions:
%e A325849 (1) (2) (3) (4) (5) (6) (7) (8)
%e A325849 (12) (13) (14) (15) (16) (17)
%e A325849 (21) (31) (23) (24) (25) (26)
%e A325849 (32) (42) (34) (35)
%e A325849 (41) (51) (43) (53)
%e A325849 (132) (52) (62)
%e A325849 (213) (61) (71)
%e A325849 (231) (124) (125)
%e A325849 (312) (142) (134)
%e A325849 (214) (143)
%e A325849 (241) (152)
%e A325849 (412) (215)
%e A325849 (421) (251)
%e A325849 (314)
%e A325849 (341)
%e A325849 (413)
%e A325849 (431)
%e A325849 (512)
%e A325849 (521)
%t A325849 Table[Length[Select[Join@@Permutations/@Select[IntegerPartitions[n],UnsameQ@@#&],!MemberQ[Differences[#,2],0]&]],{n,0,30}]
%Y A325849 The non-strict case is A238423.
%Y A325849 Cf. A007862, A049988, A175342, A279945, A295370, A325545, A325874, A325875.
%K A325849 nonn
%O A325849 0,4
%A A325849 _Gus Wiseman_, May 31 2019