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 A047695 #15 Jun 22 2024 22:25:03
%S A047695 0,1,2,8,24,260,8672
%N A047695 Nonnegative y such that y^2 = C(x,0) + C(x,1) + C(x,2) + C(x,3) is soluble in integers.
%D A047695 R. K. Guy, Unsolved Problems in Number Theory, Section D3.
%F A047695 a(n) = sqrt(A000125(A047694(n))), where sqrt = A000194 or A000196. - _M. F. Hasler_, Jun 22 2024
%e A047695 For y = 8, we have 8^2 = 64 = 1 + 7 + 21 + 35 = Sum_{k=0..3} C(x, k) for x = 7.
%t A047695 r[x_] := Reduce[y >= 0 && 6*y^2 == (x + 1)*(x^2 - x + 6), {y}, Integers]; Reap[ Do[ If[r[x] =!= False, Sow[y /. ToRules[r[x]]]], {x, -10, 1000}]][[2, 1]] (* _Jean-François Alcover_, Jul 12 2012 *)
%o A047695 (PARI) A047695=[y|n<-[-1..777], issquare(binomial(n+1, 3)+n+1,&y)] \\ _M. F. Hasler_, Jun 22 2024
%Y A047695 Cf. A047694 (the corresponding x values).
%K A047695 nonn,fini,full,nice
%O A047695 0,3
%A A047695 _N. J. A. Sloane_