A302186
Number of 3D walks of type ace.
Original entry on oeis.org
1, 3, 11, 44, 188, 842, 3911, 18692, 91412, 455540, 2306028, 11829424, 61375408, 321583108, 1699500055, 9049714852, 48513809796, 261638920412, 1418673379052, 7730011715760, 42305916178288, 232475082183544, 1282208011668988, 7096065370945168, 39394821683770960, 219341739839760912
Offset: 0
Cf.
A000108,
A000984,
A002212,
A002896,
A005572,
A026375,
A064037,
A081671,
A138547,
A145847,
A145867 (number of 3D walks of type acd),
A150500,
A202814.
-
from math import comb as binomial
def C(n): return (binomial(2*n, n)//(n+1)) # Catalan numbers
def row(n: int) -> list[int]:
return sum(binomial(n, k)*sum(binomial(k, j)*C((j+1)//2)*C(j//2)*(2*(j//2)+1) for j in range(k+1)) for k in range(n+1))
for n in range(26): print(row(n)) # Mélika Tebni, Nov 29 2024
A302187
Number of 3D walks of type bcc.
Original entry on oeis.org
1, 2, 8, 30, 138, 620, 3060, 14910, 76650, 390852, 2063376, 10832052, 58264668, 312123240, 1702423008, 9256786110, 51036229530, 280696824980, 1560925457520, 8663089672380, 48512836025940, 271229902496280, 1527733861191720, 8593482390429300, 48642125421855420, 275014629509319000
Offset: 0
Cf.
A000108,
A000984,
A002212,
A002896,
A005572,
A026375,
A064037,
A081671,
A138547,
A145847,
A145867,
A150500,
A202814.
-
from math import comb as binomial
def a(n):
return sum(binomial(n, k)*binomial(k, k//2)*binomial(n-k, (n-k)//2)**2 for k in range(n+1))
print([a(n) for n in range(26)]) # Mélika Tebni, Nov 25 2024
A302188
Number of 3D walks of type bce.
Original entry on oeis.org
1, 3, 12, 53, 252, 1252, 6416, 33609, 178996, 965660, 5263728, 28936404, 160204336, 892313424, 4995832640, 28096475977, 158638993476, 898844200524, 5108695394096, 29117034808980, 166370716319088, 952789631705104, 5467881256289856, 31438798094242244, 181079794531199440, 1044651995141484912
Offset: 0
Cf.
A000108,
A000984,
A002212,
A002896,
A005572,
A026375,
A064037,
A081671,
A138547,
A145847,
A145867,
A150500,
A202814.
-
from math import comb as binomial
def a(n):
return sum(binomial(n, k)*sum(binomial(k, j)*binomial(j, j//2)**2 for j in range(k+1)) for k in range(n+1))
print([a(n) for n in range(26)]) # Mélika Tebni, Nov 28 2024
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