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 A377850 #26 Apr 02 2025 04:43:51 %S A377850 1,2,3,4,6,5,8,7,11,10,9,12,13,17,18,14,15,19,20,26,27,16,22,21,29,28, %T A377850 38,37,24,23,31,30,40,39,51,50,25,32,33,41,42,52,53,65,66,34,35,43,44, %U A377850 54,55,67,68,82,83,36,46,45,57,56,70,69,85,84,102,101,48,47,59,58,72,71,87,86 %N A377850 Noll index series of Zernike polynomials converted to Fringe index. %C A377850 Fringe indices of Zernike polynomials sorted by Noll index. %H A377850 Gerhard Ramsebner, <a href="/A377850/b377850.txt">Table of n, a(n) for n = 1..10000</a> %H A377850 Gerhard Ramsebner, <a href="/A377850/a377850.pdf">Noll index series of Zernike polynomials converted to Fringe index</a> %H A377850 Gerhard Ramsebner, <a href="/A377850/a377850.svg">Noll index (animated SVG)</a> %H A377850 Gerhard Ramsebner, <a href="/A377850/a377850_1.svg">Fringe index (animated SVG)</a> %H A377850 Gerhard Ramsebner, <a href="/A377850/a377850_2.svg">Plot</a> %F A377850 a(j) = (1+(n+abs(m))/2)^2-2*abs(m)+[m<0] where n=floor((sqrt(8*(j-1)+1)-1)/2), m=(-1)^j*(mod(n,2)+2*floor((j-n*(n+1)/2-1+mod(n+1,2))/2)) and [] is the Iverson bracket. %F A377850 a(A176988(j)) = A375510(j) assuming offset 1 in all 3 sequences and serialized versions. %e A377850 Noll indices Fringe indices %e A377850 1 1 %e A377850 3 2 3 2 %e A377850 5 4 6 6 4 5 %e A377850 9 7 8 10 11 8 7 10 %e A377850 15 13 11 12 14 18 13 9 12 17 %e A377850 ... ... %o A377850 (PARI) A377850(j) = my(n=floor( (sqrt(8*(j-1)+1)-1)/2 ), m=(-1)^j*(n%2+2*floor((j-n*(n+1)/2-1+(n+1)%2)/2))); (1+(n+abs(m))/2)^2 -2*abs(m)+(m<0); %Y A377850 Cf. A176988, A375510. %K A377850 nonn,easy %O A377850 1,2 %A A377850 _Gerhard Ramsebner_, Nov 09 2024