A327611 Number of length n reversible string structures that are not palindromic using exactly four different colors.

0, 0, 0, 1, 6, 37, 182, 876, 3920, 17175, 73030, 306296, 1266916, 5198207, 21180642, 85909216, 347179440, 1399443775, 5629876910, 22616222616, 90754709276, 363889980927, 1458171985402, 5840531023856, 23385647663560, 93613189390175, 374664530448390

Offset

1,5

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (8,-10,-60,145,100,-470,120,456,-288).

Formula

a(n) = A056328(n) - A000453(ceiling(n/2), 4).

a(n) = 8*a(n-1) - 10*a(n-2) - 60*a(n-3) + 145*a(n-4) + 100*a(n-5) - 470*a(n-6) + 120*a(n-7) + 456*a(n-8) - 288*a(n-9) for n > 9.

G.f.: x^4*(1 - 2*x - x^2 + 6*x^3 + 5*x^4 - 18*x^5)/((1 - x)*(1 - 2*x)*(1 + 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 2*x^2)*(1 - 3*x^2)).

Prog

(PARI) concat([0, 0, 0], Vec((1 - 2*x - x^2 + 6*x^3 + 5*x^4 - 18*x^5)/((1 - x)*(1 - 2*x)*(1 + 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 2*x^2)*(1 - 3*x^2)) + O(x^30))) \\ Andrew Howroyd, Sep 18 2019

Crossrefs

Column k=4 of A309748.

Cf. A000453, A056328, A284949, A327610.

Sequence in context: A338708 A129552 A293800 * A056338 A056328 A156185

Adjacent sequences: A327608 A327609 A327610 * A327612 A327613 A327614

Keyword

nonn,easy

Author

Andrew Howroyd, Sep 18 2019

Status

approved