|
%I #8 Sep 30 2019 11:59:32
%S 0,0,0,1,6,37,182,876,3920,17175,73030,306296,1266916,5198207,
%T 21180642,85909216,347179440,1399443775,5629876910,22616222616,
%U 90754709276,363889980927,1458171985402,5840531023856,23385647663560,93613189390175,374664530448390
%N Number of length n reversible string structures that are not palindromic using exactly four different colors.
%H Andrew Howroyd, <a href="/A327611/b327611.txt">Table of n, a(n) for n = 1..200</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (8,-10,-60,145,100,-470,120,456,-288).
%F a(n) = A056328(n) - A000453(ceiling(n/2), 4).
%F 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.
%F 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)).
%o (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
%Y Column k=4 of A309748.
%Y Cf. A000453, A056328, A284949, A327610.
%K nonn,easy
%O 1,5
%A _Andrew Howroyd_, Sep 18 2019
|
