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A358653
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a(n) is the number of trivial braids on 3 strands which are products of n generators a, b, where a = sigma_1 sigma_2 sigma_1 and b = sigma_1 sigma_2.
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0
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1, 0, 4, 0, 28, 10, 244, 210, 2412, 3366, 26014, 49456, 299452, 701818, 3624478
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OFFSET
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0,3
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COMMENTS
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In the discussion of A354602, Andrey Zabolotskiy asked what the values of the sequence would be if expressed in terms of a and b. This sequence lists these values.
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LINKS
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PROG
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(SageMath)
B.<s1, s2> = BraidGroup(3)
gen = [s1*s2*s1, s1*s2]
gen += [x^-1 for x in gen]
e = B(())
words, a = {e: 1}, [1]
for n in range(15):
old_words, words = words, {}
for w, c in old_words.items():
for g in gen:
nw = w*g
words[nw] = words.get(nw, 0) + c
a.append(words.get(e, 0))
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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