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%I #16 Mar 09 2024 13:00:59
%S 0,0,12,138,1056,7050,44472,273378,1659936,10018650,60289032,
%T 362265618,2175188016,13055911050,78349815192,470141937858,
%U 2820980767296,16926272024250,101558794406952,609356253226098,3656147979709776,21936919259318250,131621609699088312
%N The sequence A059515(3,n). Number of ways of placing n identifiable nonnegative intervals with a total of exactly three starting and/or finishing points.
%H IBM Ponder This, <a href="http://domino.watson.ibm.com/Comm/wwwr_ponder.nsf/challenges/January2001.html">Jan 01 2001</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,-27,18).
%F a(n) = A058809(n)+A059116(n) = 6^n-3*3^n+3 (for n>0).
%F a(n) = 10*a(n-1)-27*a(n-2)+18*a(n-3) for n>3. - _Colin Barker_, Sep 13 2014
%F G.f.: -6*x^2*(3*x+2) / ((x-1)*(3*x-1)*(6*x-1)). - _Colin Barker_, Sep 13 2014
%e a(2)=12 since if aA indicates a zero length interval and a-A one of positive length the possibilities are: aA-b-B, b-aA-B, b-B-aA, bB-a-A, a-bB-A, a-A-bB, ab-A-B, ab-B-A, a-b-AB, b-a-AB, a-bA-B, b-a-AB.
%o (PARI) concat([0,0], Vec(-6*x^2*(3*x+2)/((x-1)*(3*x-1)*(6*x-1)) + O(x^100))) \\ _Colin Barker_, Sep 13 2014
%Y Cf. A059516.
%K nonn,easy
%O 0,3
%A _Henry Bottomley_, Jan 19 2001
%E More terms from _Colin Barker_, Sep 13 2014
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