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 A290820 Side length of the smallest equilateral triangles that have a separated dissection into n equilateral triangles with integer sides, or 0 if no such triangle exists. 3
 1, 0, 0, 2, 0, 3, 4, 4, 6, 5, 8, 6, 6, 7, 8, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS No solution exists for n = [2, 3, 5]. The meaning of "separated dissection" is defined at the end of the introduction of the Drapal and Hamalainen article, see link. - Hugo Pfoertner, Feb 17 2018 LINKS Stuart Anderson, An Introduction to Triangled Equilateral Triangles Ales Drapal, Carlo Hamalainen, An enumeration of equilateral triangle dissections, arXiv:0910.5199 [math.CO], 2009-2010. Hugo Pfoertner, Illustration for a(16)=7. EXAMPLE a(6) = 3:         *        / \       *---*      / \ / \     *---*   +    / \ /     \   *---*---+---* a(7) = 4:           *          / \         +   +        /     \       *---*---*      / \ / \ / \     +   *---*   +    /     \ /     \   *---+---*---+---* a(8) = 4:           *          / \         *---*        / \ / \       *---*   +      / \ /     \     *---*       +    / \ /         \   *---*---+---+---* a(9) = 6:               *              / \             +   +            /     \           *---+---*          / \     / \         +   +   +   +        /     \ /     \       *---+---*       +      / \     /         \     *---*   +           +    / \ / \ /             \   *---*---*---+---+---+---* a(10) = 5:             *            / \           *---*          / \ / \         *---*   +        / \ /     \       *---*       +      / \ /         \     *---*           +    / \ /             \   *---*---+---+---+---* a(11) = 8:                   *                  / \                 +   +                /     \               *---+---*              / \     / \             +   +   +   +            /     \ /     \           *---+---*       +          / \     /         \         +   +   +           +        /     \ /             \       *---+---*               +      / \     /                 \     *---*   +                   +    / \ / \ /                     \   *---*---*---+---+---+---+---+---* a(12) = 6:               *              / \             *---*            / \ / \           *---*   +          / \ /     \         *---*       +        / \ /         \       *---*           +      / \ /             \     *---*               +    / \ /                 \   *---*---+---+---+---+---* a(13) = 6:               *              / \             +   +            /     \           *---+---*          / \     / \         +   +   *---*        /     \ / \ / \       *---*---*---*   +      / \ / \     /     \     *---*   +   +       +    / \ /     \ /         \   *---*---+---*---+---+---* a(14) = 7:                 *                / \               +   +              /     \             +       +            /         \           *---+---*---*          / \     / \ / \         +   +   *---*   +        /     \ / \ /     \       *---*---*---*       +      / \ / \     /         \     *---*   +   +           +    / \ /     \ /             \   *---*---+---*---+---+---+---* a(15) = 8:                   *                  / \                 +   +                /     \               *---+---*              / \     / \             +   +   *---*            /     \ / \ / \           +       *---*   +          /         \ /     \         *---+---+---*       +        / \         /         \       *---*       +           +      / \ / \     /             \     *---*   +   +               +    / \ /     \ /                 \   *---*---+---*---+---+---+---+---* a(16) = 7:                 *                / \               +   +              /     \             *---+---*            / \     / \           +   +   *---*          /     \ / \ / \         *---*---*---*---*        / \ / \         / \       *---*   +       +   +      / \ /     \     /     \     *---*       +   +       +    / \ /         \ /         \   *---*---+---+---*---+---+---* CROSSREFS Cf. A167123, A290653, A290697, A290821. Sequence in context: A137218 A306765 A087819 * A278029 A066246 A198370 Adjacent sequences:  A290817 A290818 A290819 * A290821 A290822 A290823 KEYWORD nonn,more AUTHOR Hugo Pfoertner, Aug 11 2017 EXTENSIONS Title changed as suggested by Peter Munn, Feb 17 2018 STATUS approved

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Last modified March 30 19:49 EDT 2020. Contains 333127 sequences. (Running on oeis4.)