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 A241201 #8 Dec 14 2020 18:59:38
%S A241201 7,14,62,31,339,1022
%N A241201 a(n) is the least r such that there are n+2 consecutive increasing terms in the r-th row of Pascal's triangle (binomial(r,*)) which satisfy a polynomial of degree n.
%C A241201 Old definition: "Numbers k such that n+2 consecutive terms of binomial(n,k) satisfy a polynomial relation of degree n for some k in the range 0 <= k <= n/2.".
%C A241201 Is this sequence finite?
%e A241201 a(1) = 7 because the 3 terms 7, 21, 35 are linear.
%t A241201 t = Table[k = 1; While[b = Binomial[k, Range[0, k/2]]; d = Differences[b, n + 1]; ! MemberQ[d, 0], k++]; {k, Position[d, 0, 1, 1][[1, 1]] - 1}, {n, 6}]; Transpose[t][[1]]
%Y A241201 Cf. A008865 (binomial(n,k) has 3 consecutive terms in a linear relation).
%Y A241201 Cf. A062730 (3 terms in arithmetic progression in Pascal's triangle).
%Y A241201 Cf. A241199, A241200 (similar, but quadratic).
%Y A241201 Cf. A241202 (position of the first of terms).
%K A241201 nonn,more
%O A241201 1,1
%A A241201 _T. D. Noe_, Apr 21 2014
%E A241201 Definition clarified by _Don Reble_, Dec 14 2020