A130515 -id:A130515 - cp's OEIS frontend

A130516 In triangular peg solitaire, number of distinct solvable feasible pairs starting with one peg missing and finishing with one peg.

0, 0, 1, 12, 29, 27, 80, 125, 108, 260, 356, 300, 637, 832, 675, 1341, 1665, 1323, 2500, 3025, 2352, 4304, 5072, 3888, 6929, 8036, 6075, 10625, 12125, 9075, 15616, 17629, 13068, 22212, 24804, 18252, 30685, 34000, 24843, 41405, 45521

Offset: 2

N. J. A. Sloane, Aug 09 2007

nonn

Coincides with A130515 for n >= 6.

George I. Bell, Table of n, a(n) for n = 2..52
George I. Bell, Solving Triangular Peg Solitaire [arXiv:math/0703865v4]
G. I. Bell, Solving Triangular Peg Solitaire, JIS 11 (2008) 08.4.8

Cf. A130515.

Reference gives an explicit formula for a(n).

More terms from George I. Bell (gibell(AT)comcast.net), Sep 27 2007

A355295 Number of distinct board states reachable in n jumps in European Peg Solitaire.

Original entry on oeis.org

1, 4, 17, 92, 495, 2475, 11771, 52226, 212527, 789228, 2640323, 7870055, 20730606, 47916748, 96715832, 170154214, 260956703, 349541944, 410294786, 423631649, 385887175, 310724581, 221398196, 139580751, 77748102, 38162987, 16445627, 6178002, 2007607, 559163, 131269, 25378, 4012, 481, 36, 4

Offset: 0

Sander G. Huisman, Jun 27 2022

			The beginning state is missing the peg just above the center, as an initial state with the center peg removed does not yield any valid solutions where 1 peg is remaining.
       * * *
     * * * * *
   * * * O * * *
   * * * * * * *
   * * * * * * *
     * * * * *
       * * *
The next move yields the next 4 states:
       * * *             * * *             * O *             * * *
     * * * * *         * * * * *         * * O * *         * * * * *
   * O O * * * *     * * * * * * *     * * * * * * *     * * * * O O *
   * * * * * * *     * * * O * * *     * * * * * * *     * * * * * * *
   * * * * * * *     * * * O * * *     * * * * * * *     * * * * * * *
     * * * * *         * * * * *         * * * * *         * * * * *
       * * *             * * *             * * *             * * *

Sander G. Huisman, Mathematica program for this sequence

Cf. A335656, A351286, A112737, A130515, A350561.

cp's OEIS Frontend

A130516 In triangular peg solitaire, number of distinct solvable feasible pairs starting with one peg missing and finishing with one peg.

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