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 A381451 #31 Aug 15 2025 15:54:59 %S A381451 1,1,1,1,2,1,1,3,3,1,1,4,6,4,1,1,5,9,9,5,1,1,6,12,14,12,6,1,1,7,16,25, %T A381451 25,16,7,1,1,8,20,40,46,40,20,8,1,1,9,25,56 %N A381451 Triangle read by rows: T(n,k) is the clique covering number of the Johnson graph J(n, k), n >= 2, 0 < k < n. %C A381451 T(2*k, k) = C(k) = A000108(k), the k-th Catalan number, for k = 1, 2, 4, 6, 8, 16; whether this holds for other values of k is an open question. %H A381451 Søren Fuglede Jørgensen, <a href="https://doi.org/10.1007/s10623-025-01663-3">On the clique covering numbers of Johnson graphs</a>, Des. Codes Cryptogr. (2025); <a href="https://arxiv.org/abs/2502.15019">arXiv:2502.15019</a> [math.CO], 2025. %H A381451 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CliqueCoveringNumber.html">Clique Covering Number</a>. %H A381451 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/JohnsonGraph.html">Johnson Graph</a>. %H A381451 Wikipedia, <a href="https://en.wikipedia.org/wiki/Johnson_graph">Johnson graph</a>. %F A381451 T(n, k) = T(n, n - k). %F A381451 T(n, 1) = 1. %F A381451 T(n, 2) = n - 2. %F A381451 T(n, 3) = A002620(n-1), for n >= 6. %F A381451 T(n, k) <= T(n - 1, k - 1) + T(n - 1, k). %e A381451 Triangle begins: %e A381451 n\k 1 2 3 4 5 6 7 8 9 10 %e A381451 2: 1 %e A381451 3: 1 1 %e A381451 4: 1 2 1 %e A381451 5: 1 3 3 1 %e A381451 6: 1 4 6 4 1 %e A381451 7: 1 5 9 9 5 1 %e A381451 8: 1 6 12 14 12 6 1 %e A381451 9: 1 7 16 25 25 16 7 1 %e A381451 10: 1 8 20 40 46 40 20 8 1 %e A381451 11: 1 9 25 56 ? ? 56 25 9 1 %e A381451 ... %Y A381451 Cf. A002620 (column 3). %K A381451 nonn,tabl,hard,more %O A381451 2,5 %A A381451 _Søren Fuglede Jørgensen_, Feb 24 2025