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 A363910 #24 Dec 30 2023 19:59:36 %S A363910 1,0,2,0,2,6,0,6,14,22,0,28,56,86,92,0,162,298,428,518,422,0,1076, %T A363910 1868,2562,3096,3144,2074,0,7852,13076,17292,20624,21990,19366,10754 %N A363910 Triangular array read by rows: T(n,k) = the number of closed meanders with n top arches and k closed meanders in the reduction of the closed meander by the reverse of the exterior arch splitting algorithm. %C A363910 The terms of this sequence can also be derived from sequences of consecutively numbered stamps folded with stamp 1 on top. %F A363910 T(n,n) = A001181(n). %F A363910 T(n,2) = A005316(2*n-4)*2 for n > 1. %e A363910 n\k 1 2 3 4 5 6 7 8 %e A363910 1: 1 %e A363910 2: 0 2 %e A363910 3: 0 2 6 %e A363910 4: 0 6 14 22 %e A363910 5: 0 28 56 86 92 %e A363910 6: 0 162 298 428 518 422 %e A363910 7: 0 1076 1868 2562 3096 3144 2074 %e A363910 8: 0 7852 13076 17292 20624 21990 19366 10754 %e A363910 Closed meander: Closed meander split with bottom rotated right %e A363910 4 top arches to form top of semi-meander with 8 arches %e A363910 ______ ______ %e A363910 / ____ \ / ____ \ %e A363910 / / __ \ \ / / __ \ \ __ %e A363910 / / / \ \ \ / / / \ \ \ / \ %e A363910 / / / /\ \ \ \ / / / /\ \ \ \ /\ /\ / /\ \ %e A363910 \ \/ / \/ \/ binary representation of semi-meander %e A363910 \__/ 1 1 1 1 0 0 0 0 1 0 1 0 1 1 0 0 %e A363910 Semi-meander top arches with no covering center arch = cm %e A363910 START: center | %e A363910 Reduction of semi-meander: 1 1 1 1 0 0 0 0 1 0 1 0 1 1 0 0 cm(1) %e A363910 Combine end of first arch 1 1 1 1 0 0 0 0e 1 0 1 0 1s 1 0 0 %e A363910 Oe with beginning of last 1 1 1 0 0 0 1 1 0 1 0 0 1 0 %e A363910 arch 1s. 0e...1s becomes 1 1 1 0 0 0e 1 1 0 1 0 0 1s 0 %e A363910 1...0 in the next line. The 1 1 0 0 1 1 1 0 1 0 0 0 %e A363910 starting 1 and ending 0 1 1 0 0e 1s 1 1 0 1 0 0 0 %e A363910 are removed in the next line 1 0 1 0 1 1 0 1 0 0 %e A363910 reducing number of arches. 1 0e 1 0 1s 1 0 1 0 %e A363910 by one. 1 1 0 0 1 0 1 0 cm(2) %e A363910 1 1 0 0e 1 0 1s 0 %e A363910 1 0 1 1 0 0 %e A363910 1 0e 1s 1 0 0 %e A363910 1 0 1 0 cm(3) %e A363910 Example: T(4,3) 4 starting top arches with 3 closed meanders in history. %Y A363910 Cf. A005315 (row sums), A001181, A005316, A000682. %K A363910 nonn,tabl,more %O A363910 1,3 %A A363910 _Roger Ford_, Jun 27 2023