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 A134563 #12 Jan 05 2025 19:51:38 %S A134563 1,2,5,3,7,18,4,8,24,59,6,10,26,78,188,9,11,27,84,248,594,13,12,33,86, %T A134563 267,783,1872,19,14,35,87,273,843 %N A134563 Array read by antidiagonals: row n consists of numbers whose 3rd-order Zeckendorf representation has exactly n terms. %C A134563 A permutation of the natural numbers. %H A134563 C. Kimberling, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/33-1/kimberling.pdf">The Zeckendorf array equals the Wythoff array</a>, Fibonacci Quarterly 33 (1995) 3-8. %H A134563 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a> %F A134563 Row 1, A000930, is the 3rd-order Zeckendorf basis, b(1), b(2), b(3), .... Every positive integer has a unique 3rd-order Zeckendorf representation b(i(1)) + b(i(2)) + ... + b(i(n)), where |i(h) - i(j)| >=3 for distinct h and j. %e A134563 Northwest corner of the array: %e A134563 1 2 3 4 6 9 13 19 28 41 60 88 129 ... %e A134563 5 7 8 10 11 12 ... %e A134563 18 24 26 27 33 35 ... %e A134563 59 78 84 86 87 106 ... %e A134563 For example, 26=19+6+1 has 3 terms, so 26 is in row 3. %Y A134563 Cf. A000930, A136189, A134564. %K A134563 nonn,tabl %O A134563 1,2 %A A134563 _Clark Kimberling_, Nov 01 2007, Dec 18 2007