A288687 Number of n-digit biquanimous strings using digits {0,1,2,3}.

1, 1, 4, 19, 92, 421, 1830, 7687, 31624, 128521, 518666, 2084875, 8361996, 33497101, 134094862, 536608783, 2146926608, 8588754961, 34357248018, 137433710611, 549744803860, 2199000186901, 8796044787734, 35184271425559, 140737278640152, 562949517213721

Offset: 0

Author

Alois P. Heinz, Jun 13 2017

Keywords

• nonn
• easy

Comments

A biquanimous string is a string whose digits can be split into two groups with equal sums.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-37,64,-52,16).

Crossrefs

Column k=3 of A288638.

Programs

Mathematica

LinearRecurrence[{10,-37,64,-52,16},{1,1,4,19,92,421},30] (* Harvey P. Dale, Jul 29 2017 *)

PARI

Vec((1 - 9*x + 31*x^2 - 48*x^3 + 38*x^4 - 16*x^5) / ((1 - x)^2*(1 - 2*x)^2*(1 - 4*x)) + O(x^30)) \\ Colin Barker, Dec 16 2017

Formula

G.f.: (1 - 9*x + 31*x^2 - 48*x^3 + 38*x^4 - 16*x^5) / ((1 - x)^2*(1 - 2*x)^2*(1 - 4*x)).

a(n) = 1 + A064671(n) for n > 0.

From Colin Barker, Dec 16 2017: (Start)

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

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)