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 A383549 #14 May 04 2025 03:21:30
%S A383549 0,0,0,1,1,2,5,3,9,11,10,24,21,30,50,43,75,93,96,161,170,215,312,323,
%T A383549 456,574,639,906,1046,1276,1710,1935,2501,3135,3642,4760,5699,6893,
%U A383549 8823,10401,12952,16079,19104,24002,29097,35165,43865,52628,64503,79363,95329
%N A383549 Number of rises in all compositions of n with parts in {1,2,3} and adjacent differences in {-1,1}.
%C A383549 A rise is any pair of parts (p_{i-1},p_i) with p_{i-1} < p_i.
%C A383549 By reversal a(n) is also the number of descents in all compositions of n of this kind.
%H A383549 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,0,2,-1,0,-2,0,-1).
%F A383549 G.f.: x^3*(1 + x^2)^2*(1 + x + x^3)/(1 - x^3 - x^5)^2.
%e A383549 For n = 6 the following compositions have 5 rises: (1,2,1,2), (1,2,3), (2,1,2,1), (3,2,1).
%o A383549 (PARI)
%o A383549 A_x(N) = {my(x='x+O('x^N)); concat([0,0,0], Vec(x^3*(1 + x^2)^2*(1 + x + x^3)/(1 - x^3 - x^5)^2))}
%o A383549 A_x(40)
%Y A383549 Cf. A011782, A076118, A124760, A151842, A173258, A214247, A220062, A238343.
%K A383549 nonn,easy
%O A383549 0,6
%A A383549 _John Tyler Rascoe_, Apr 29 2025