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

1,4

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).

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)).

Prog

(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)))

Crossrefs

Column k=3 of A309748.

Cf. A000392, A056327, A284949, A327611.

Sequence in context: A245824 A356121 A345326 * A110686 A071729 A278692

Adjacent sequences: A327607 A327608 A327609 * A327611 A327612 A327613

Keyword

nonn,easy

Author

Andrew Howroyd, Sep 18 2019

Status

approved