This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A059517 #20 Dec 02 2024 16:19:51 %S A059517 0,0,12,138,1056,7050,44472,273378,1659936,10018650,60289032, %T A059517 362265618,2175188016,13055911050,78349815192,470141937858, %U A059517 2820980767296,16926272024250,101558794406952,609356253226098,3656147979709776,21936919259318250,131621609699088312 %N A059517 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 A059517 IBM Ponder This, <a href="https://research.ibm.com/haifa/ponderthis/challenges/January2001.html">Jan 01 2001</a> %H A059517 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,-27,18). %F A059517 a(n) = A058809(n)+A059116(n) = 6^n-3*3^n+3 (for n>0). %F A059517 a(n) = 10*a(n-1)-27*a(n-2)+18*a(n-3) for n>3. - _Colin Barker_, Sep 13 2014 %F A059517 G.f.: -6*x^2*(3*x+2) / ((x-1)*(3*x-1)*(6*x-1)). - _Colin Barker_, Sep 13 2014 %e A059517 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 A059517 (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 A059517 Cf. A059516. %K A059517 nonn,easy %O A059517 0,3 %A A059517 _Henry Bottomley_, Jan 19 2001 %E A059517 More terms from _Colin Barker_, Sep 13 2014