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A064671
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Number of n-digit base 4 biquanimous numbers (with leading 0's allowed, but not all-0 string).
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2
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0, 3, 18, 91, 420, 1829, 7686, 31623, 128520, 518665, 2084874, 8361995, 33497100, 134094861, 536608782, 2146926607, 8588754960, 34357248017, 137433710610, 549744803859, 2199000186900, 8796044787733, 35184271425558, 140737278640151, 562949517213720
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OFFSET
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1,2
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COMMENTS
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A number is biquanimous (A064544) if its digits can be split into two groups with the same sum. - David W. Wilson, SeqFan memo, Oct 08 2001.
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LINKS
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FORMULA
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Empirical g.f.: x^2*(3 - 12*x + 22*x^2 - 16*x^3) / ((1 - x)^2*(1 - 2*x)^2*(1 - 4*x)). [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]
a(n) = (2^n-2) * (1+2^n-n) / 2.
a(n) = 10*a(n-1) - 37*a(n-2) + 64*a(n-3) - 52*a(n-4) + 16*a(n-5) for n>5.
(End)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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