OFFSET
0,3
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).
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)
MATHEMATICA
LinearRecurrence[{10, -37, 64, -52, 16}, {1, 1, 4, 19, 92, 421}, 30] (* Harvey P. Dale, Jul 29 2017 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Jun 13 2017
STATUS
approved