A302183 Number of 3D n-step walks of type abd.
1, 1, 4, 10, 39, 131, 521, 1989, 8149, 33205, 139870, 592120, 2552155, 11079303, 48639722, 214997228, 957817013, 4292316197, 19349957108, 87663905954, 399038606291, 1823961268751, 8369603968599, 38540835938335, 178056111047329, 825079806039121, 3833960405339446
Offset: 0
Links
- Nachum Dershowitz, Touchard's Drunkard, Journal of Integer Sequences, Vol. 20 (2017), #17.1.5.
Crossrefs
Programs
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Python
from math import comb as binomial def M(n): return sum(binomial(n, 2*k)*binomial(2*k, k)//(k+1) for k in range(n//2+1)) # Motzkin numbers def a(n): return sum(binomial(n, k)*binomial(k, k//2)*((k+1) %2)*M(n-k) for k in range(n+1)) print([a(n) for n in range(27)]) # Mélika Tebni, Dec 03 2024
Formula
From Mélika Tebni, Dec 03 2024: (Start)
Inverse binomial transform of A302184. (End)
Extensions
a(13)-a(26) from Mélika Tebni, Dec 03 2024
Comments