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A327611 Number of length n reversible string structures that are not palindromic using exactly four different colors. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 17 04:36 EDT 2021. Contains 343059 sequences. (Running on oeis4.)