A327610 Number of length n reversible string structures that are not palindromic using exactly three different colors.

0, 0, 1, 4, 14, 49, 154, 496, 1520, 4705, 14266, 43384, 130844, 394849, 1187614, 3571936, 10729040, 32222785, 96724306, 290313064, 871172324, 2614069249, 7843168774, 23531688976, 70598997560, 211805640865, 635432906746, 1906333059544, 5719063904204

Offset: 1

Author

Andrew Howroyd, Sep 18 2019

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (6,-6,-24,49,6,-66,36).

Crossrefs

Column k=3 of A309748.

Cf. A000392, A056327, A284949, A327611.

Programs

PARI

concat([0,0], Vec((1 - 2*x - 4*x^2 + 13*x^3 - 9*x^4)/((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 2*x^2)*(1 - 3*x^2)) + O(x^30)))

Formula

a(n) = A056327 - A000392(ceiling(n/2)).

a(n) = 6*a(n-1) - 6*a(n-2) - 24*a(n-3) + 49*a(n-4) + 6*a(n-5) - 66*a(n-6) + 36*a(n-7) for n > 7.

G.f.: x^3*(1 - 2*x - 4*x^2 + 13*x^3 - 9*x^4)/((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 2*x^2)*(1 - 3*x^2)).