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

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

Offset: 1

Author

John W. Layman, Oct 09 2001

Keywords

• nonn
• base

Comments

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.

Formula

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]

Conjectures from Colin Barker, Dec 16 2017: (Start)

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)

Extensions

More terms from Christian G. Bower, Oct 12 2001