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 A265507 A pyramid T(n,p,k) of square arrays read by rows relating semimeanders(n), positive arches(p) and components(k). 0
 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 0, 1, 0, 5, 0, 0, 2, 0, 4, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 8, 0, 1, 0, 9, 0, 10, 0, 2, 0, 8, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 13, 0, 0, 1, 0, 13, 0, 36, 0, 0, 3, 0, 23, 0, 24, 0, 0, 3, 0, 12, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,11 COMMENTS A positive arch is defined as a top arch that starts at an odd-numbered vertex and ends at a higher even-numbered vertex. For each value of n there is a square array with n^2 elements. Rows are in order of decreasing number of components. The sum of all the elements in each square array(n) = Catalan numbers C(n) A000108. The sum of columns for array(n) = Semimeander components row(n) A046726. The sum of the rows for array(n) = Narayana numbers T(n,k) A001263. All semimeander solutions (k=1) for array n have positive arches = floor((n+2)/2). LINKS EXAMPLE For n=3:                                   /\          /\                /\               /\        /  \        //\\               /  \             /  \      /    \      //  \\   /\ /\ /\   / /\ \  /\   /\  / /\ \    //\  /\\    // /\ \\   \ \\// /   \ \ \/ / /   \ \ \/ / /    \\ \/ //    \\ \/ //    \ \/ /     \ \  / /     \ \  / /      \\  //      \\  //     \  /       \ \/ /       \ \/ /        \\//        \\//      \/         \  /         \  /          \/          \/                  \/           \/   p=3,k=2     p=2,k=1      p=2,k=1      p=1,k=2     p=2,k=3. . n=3  p\k 3  2  1   n=9  p\k 9  8  7  6  5  4  3  2  1       1: 0  1  0         1: 0  0  0  0  1  0  0  0  0       2: 1  0  2         2: 0  0  0  4  0 32  0  0  0       3: 0  1  0         3: 0  0  6  0 78  0 252 0  0                          4: 0  4  0 72  0 446 0 654 0                          5: 1  0 29  0 280 0 950 0 504                          6: 0  4  0 72  0 446 0 654 0                          7: 0  0  6  0 78  0 252 0  0                          8: 0  0  0  4  0 32  0  0  0                          9: 0  0  0  0  1  0  0  0  0 CROSSREFS Cf. A000108, A001263, A046726. Sequence in context: A123858 A193261 A283497 * A035145 A244315 A214303 Adjacent sequences:  A265504 A265505 A265506 * A265508 A265509 A265510 KEYWORD nonn,tabf AUTHOR Roger Ford, Dec 09 2015 STATUS approved

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Last modified September 18 02:19 EDT 2020. Contains 337164 sequences. (Running on oeis4.)