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 A174084 #10 May 19 2025 08:16:05 %S A174084 21,94,544,3509,26799,223123,2133511,21793042,248348572,3008632130, %T A174084 39989075942,558800689295 %N A174084 Number of permutations of length n with no consecutive triples i,...i+r,...i+2r for all positive r, and for all equal spacings d. %C A174084 Here we count both the sequence 1,2,3 (r=1) as a progression in 1,2,3,0,4,5, (note d=1) and in 1,0,2,4,3,5 (here, d=2). %e A174084 For n=4 there are 4!-a(4)=3 with some progression. These are (0,1,2,3), (1,2,3,0), and (3,0,1,2). Here for all the progressions, r=1 and d=1, hence this term is the same as a(4) in A002628. %Y A174084 Cf. A002628, A174080, A174085, A174086, A174087. %K A174084 nonn,more %O A174084 4,1 %A A174084 _Isaac Lambert_, Apr 20 2010 %E A174084 Name clarified and a(10)-a(15) from _Bert Dobbelaere_, May 19 2025