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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.)