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 A386481 #28 Aug 11 2025 23:29:35 %S A386481 1,1,1,1,1,1,1,2,2,1,1,3,7,4,1,1,4,14,16,7,1,1,5,23,34,29,11,1,1,6,34, %T A386481 58,63,46,16,1,1,7,47,88,109,101,67,22,1,1,8,62,124,167,176,148,92,29, %U A386481 1,1,9,79,166,237,271,259,204,121,37,1,1,10,98,214,319,386,400,358,269,154,46,1,1,11,119,268,413,521,571,554,473,343,191,56,1 %N A386481 Array read by upward antidiagonals: T(k,n) = 1 (k = 0, n >= 0), T(k,n) = binomial(n,2)*k^2 + n*(k-1) + 1 (k >= 1, n >= 0). %C A386481 T(k,n) is the maximum number of regions the plane can be divided into by drawing n k-armed long-legged V's. %D A386481 David O. H. Cutler and N. J. A. Sloane, paper in preparation, August 1 2025. %H A386481 N. J. A. Sloane, <a href="/A386481/a386481_1.jpg">Illustration for T(3,2) = 14.</a> %H A386481 N. J. A. Sloane, <a href="/A386481/a386481.jpg">Illustration for T(3,3) = 34 (a 3-armed V is also known as a Wu).</a> %e A386481 Array begins (the rows are T(0,n>=0),, T(1,n>=0), T(2,n>=0), ...): %e A386481 1, 1, 1, 1, 1, 1, 1, 1, 1, ... %e A386481 1, 1, 2, 4, 7, 11, 16, 22, 29, ... %e A386481 1, 2, 7, 16, 29, 46, 67, 92, 121, ... %e A386481 1, 3, 14, 34, 63, 101, 148, 204, 269, ... %e A386481 1, 4, 23, 58, 109, 176, 259, 358, 473, ... %e A386481 1, 5, 34, 88, 167, 271, 400, 554, 733, ... %e A386481 1, 6, 47, 124, 237, 386, 571, 792, 1049, ... %e A386481 1, 7, 62, 166, 319, 521, 772, 1072, 1421, ... %e A386481 ... %e A386481 The first few antidiagonals are: %e A386481 1, %e A386481 1, 1, %e A386481 1, 1, 1, %e A386481 1, 2, 2, 1, %e A386481 1, 3, 7, 4, 1, %e A386481 1, 4, 14, 16, 7, 1, %e A386481 1, 5, 23, 34, 29, 11, 1, %e A386481 1, 6, 34, 58, 63, 46, 16, 1, %e A386481 1, 7, 47, 88, 109, 101, 67, 22, 1, %e A386481 ... %Y A386481 This is a companion to the array A386478. %Y A386481 The rows and columns include A000124, A130883, A140064, A383464, and A008865. %K A386481 nonn,tabl %O A386481 0,8 %A A386481 _N. J. A. Sloane_, Aug 11 2025 %E A386481 Under construction, please do not touch.