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 A316384 Number of ways to stack n triangles symmetrically in a valley (pointing upwards or downwards depending on row parity). 5
 1, 1, 1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 4, 2, 5, 2, 5, 2, 6, 3, 8, 4, 9, 4, 10, 4, 12, 6, 15, 7, 17, 7, 19, 8, 22, 10, 26, 12, 30, 13, 33, 14, 38, 17, 45, 21, 51, 22, 56, 24, 64, 29, 74, 33, 83, 36, 92, 40, 104, 46, 119, 53, 133, 58, 147, 63, 165, 73, 187, 83, 208, 90 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS *           / \        *-*-*-*-*         \ / \ /          *---*           \ /            * Such a way to stack is not allowed. LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 FORMULA a(2n+1) = A036015(n). a(2n  ) = A036016(n). a(n) = |A029838(n)| = |A082303(n)|. Euler transform of period 16 sequence [1, 0, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 0, 1, 0, ...]. EXAMPLE a(16) = 4.                                  *   *                                 / \ / \      *---*---*---*---*         *---*---*       \ / \ / \ / \ /         / \ / \ / \        *---*---*---*         *---*---*---*         \ / \ / \ /           \ / \ / \ /          *---*---*             *---*---*           \ / \ /               \ / \ /            *---*                 *---*             \ /                   \ /              *                     *    *---*           *---*     *           *     \ / \         / \ /     / \         / \      *---*       *---*     *---*   *   *---*       \ / \     / \ /       \ / \ / \ / \ /        *---*   *---*         *---*---*---*         \ / \ / \ /           \ / \ / \ /          *---*---*             *---*---*           \ / \ /               \ / \ /            *---*                 *---*             \ /                   \ /              *                     * a(17) = 2.            *---*         *---*           *---*           / \ / \         \ / \         / \ /          *---*---*         *---*       *---*         / \ / \ / \         \ / \     / \ /        *---*---*---*         *---*---*---*         \ / \ / \ /           \ / \ / \ /          *---*---*             *---*---*           \ / \ /               \ / \ /            *---*                 *---*             \ /                   \ /              *                     * PROG (Ruby) def s(k, n)   s = 0   (1..n).each{|i| s += i if n % i == 0 && i % k == 0}   s end def A(ary, n)   a_ary = [1]   a = [0] + (1..n).map{|i| ary.inject(0){|s, j| s + j[1] * s(j[0], i)}}   (1..n).each{|i| a_ary << (1..i).inject(0){|s, j| s - a[j] * a_ary[-j]} / i}   a_ary end def A316384(n)   A([[1, 1], [4, -1]], n).map{|i| i.abs} end p A316384(100) CROSSREFS Cf. A000700 (number of symmetric Ferrers graphs with n nodes), A006950 (number of ways to stack n triangles in a valley), A029838, A036015, A036016, A082303. Sequence in context: A025825 A293224 A082303 * A029838 A213649 A242397 Adjacent sequences:  A316381 A316382 A316383 * A316385 A316386 A316387 KEYWORD nonn AUTHOR Seiichi Manyama, Jun 30 2018 STATUS approved

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Last modified April 16 04:49 EDT 2021. Contains 343030 sequences. (Running on oeis4.)