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 A270615 #20 Mar 25 2018 08:21:11 %S A270615 67,289,345,1029 %N A270615 Sporadic solutions s to the equations Sum_i (-1)^i * binomial(m,i) * binomial(s-m,t-i) = 0 listed in increasing order. %C A270615 "Sporadic" solutions s: these are the solutions that remain from A269563, when we remove the four known infinite families of solutions in polynomial progression (see the comments in A269563) and also remove all the nine known infinite families of solutions in exponential progression (see the comments in A269499). These nine families are the s = 2*m + p, where p=4,5,6 or 8 and (m,t) are positive integer solutions to some Diophantine bivariate polynomial equation of degree 2: %C A270615 p=4 m^2 - 4*m*t + 2*t^2 + 3*m - 8*t + 2 = 0 %C A270615 p=5 5*m^2 - 10*m*t + 4*t^2 + 25*m - 26*t + 32 = 0 %C A270615 p=5 m^2 - 6*m*t + 4*t^2 + 3*m - 14*t + 2 = 0 %C A270615 p=6 m^2 - 8*m*t + 4*t^2 + 3*m - 24*t + 2 = 0 %C A270615 p=8 m^2 - 4*m*t + 2*t^2 + 7*m - 16*t + 16 = 0 %C A270615 1521, 10882, 15043 and 48324 are also "sporadic" solutions, but the list has been checked to be complete up to 1029 only. %e A270615 67 is in the sequence because Sum_i (-1)^i * binomial(m,i) * binomial(67-m,t-i) = 0, when m=22 and t=5. And m=22 and t=5 do not belong to any of the above progressions. %Y A270615 Cf. A269563, A269499. %K A270615 nonn,more,hard %O A270615 1,1 %A A270615 _René Gy_, Mar 20 2016