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A305003
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Number of length-n binary words having no subwords that are abelian fourth powers.
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2
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1, 2, 4, 8, 14, 26, 48, 88, 146, 236, 394, 674, 1060, 1640, 2536, 4086, 6470, 10292, 16374, 25720, 39332, 60154, 92486, 144218, 217772, 327898, 494384, 745096, 1089186, 1587432, 2338018, 3460572, 4977860, 7197148, 10395464, 14991916, 20924630, 28852352
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OFFSET
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0,2
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COMMENTS
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An "abelian fourth power" means four contiguous nonempty blocks of the same length and same number of 0's and 1's, such as (011)(101)(110)(101).
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LINKS
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EXAMPLE
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For n = 5 the only words not counted are 00000, 00001, 10000, and their complements.
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MAPLE
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f:= proc(L)
local i, w, j;
for i from 1 to floor(nops(L)/4) do
if L[2*i]=2*L[i] and L[3*i]=3*L[i] and L[4*i]=4*L[i] then return NULL
fi
od:
L
end proc:
g:= proc(L)
local Lp;
Lp:= [0, op(L)]:
f(Lp), f(map(`+`, Lp, 1));
end proc:
S:= [0]: A[0]:= 1: A[1]:= 2:for n from 2 to 31 do
S:= map(g, S);
A[n]:= 2*nops(S);
od:
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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