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 A302183 #21 Apr 20 2025 03:49:12
%S A302183 1,1,4,10,39,131,521,1989,8149,33205,139870,592120,2552155,11079303,
%T A302183 48639722,214997228,957817013,4292316197,19349957108,87663905954,
%U A302183 399038606291,1823961268751,8369603968599,38540835938335,178056111047329,825079806039121,3833960405339446
%N A302183 Number of 3D n-step walks of type abd.
%C A302183 See Dershowitz (2017) for precise definition.
%H A302183 Nachum Dershowitz, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL20/Dershowitz/dersh3.html">Touchard's Drunkard</a>, Journal of Integer Sequences, Vol. 20 (2017), #17.1.5.
%F A302183 From _Mélika Tebni_, Dec 03 2024: (Start)
%F A302183 a(n) = Sum_{k=0..n} binomial(n, k)*A126869(k)*A001006(n-k).
%F A302183 Inverse binomial transform of A302184. (End)
%o A302183 (Python)
%o A302183 from math import comb as binomial
%o A302183 def M(n): return sum(binomial(n, 2*k)*binomial(2*k, k)//(k+1) for k in range(n//2+1)) # Motzkin numbers
%o A302183 def a(n):
%o A302183 return sum(binomial(n, k)*binomial(k, k//2)*((k+1) %2)*M(n-k) for k in range(n+1))
%o A302183 print([a(n) for n in range(27)]) # _Mélika Tebni_, Dec 03 2024
%Y A302183 Cf. A000108, A000984, A002212, A002896, A005572, A026375, A064037, A081671, A138547, A145847, A145867, A150500, A202814.
%Y A302183 Cf. A001006, A126869, A302184.
%K A302183 nonn,walk
%O A302183 0,3
%A A302183 _N. J. A. Sloane_, Apr 09 2018
%E A302183 a(13)-a(26) from _Mélika Tebni_, Dec 03 2024