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A309025
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Expansion of x * Product_{k>=0} (1 + x^(2^k) + x^(2^(k+3))).
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2
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0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 4, 2, 2, 1, 4, 2, 2, 1, 5, 3, 3, 2, 4, 2, 2, 1, 6, 3, 4, 2, 4, 2, 2, 1, 7, 4, 4, 2, 4, 2, 2, 1, 8, 4, 4, 2, 4, 2, 2, 1, 9, 5, 5, 3, 5, 3, 3, 2, 9, 4, 5, 2, 5, 2, 3, 1, 10, 6, 5, 3, 6, 4, 3, 2, 10, 4, 5, 2, 6, 2, 3, 1, 11, 7, 6, 4
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OFFSET
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0,10
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COMMENTS
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a(n+1) is the number of representations of n=sum_i c_i*2^i with c_i in {0,1,8} [Anders]. See A120562 if c_i in {0,1,3} or A000012 if c_i in {0,1}. - R. J. Mathar, Mar 01 2023
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LINKS
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FORMULA
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a(n) = 0 for n <= 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = a(n-3) + a(n+1).
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MATHEMATICA
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nmax = 100; CoefficientList[Series[x Product[(1 + x^(2^k) + x^(2^(k + 3))), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
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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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