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A064671 Number of n-digit base 4 biquanimous numbers (with leading 0's allowed, but not all-0 string). 2

%I

%S 0,3,18,91,420,1829,7686,31623,128520,518665,2084874,8361995,33497100,

%T 134094861,536608782,2146926607,8588754960,34357248017,137433710610,

%U 549744803859,2199000186900,8796044787733,35184271425558,140737278640151,562949517213720

%N Number of n-digit base 4 biquanimous numbers (with leading 0's allowed, but not all-0 string).

%C 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.

%F 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]

%F Conjectures from _Colin Barker_, Dec 16 2017: (Start)

%F a(n) = (2^n-2) * (1+2^n-n) / 2.

%F 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.

%F (End)

%K nonn,base

%O 1,2

%A _John W. Layman_, Oct 09 2001

%E More terms from _Christian G. Bower_, Oct 12 2001

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Last modified March 18 19:58 EDT 2019. Contains 321293 sequences. (Running on oeis4.)