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

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

Author

Sander G. Huisman, Jun 27 2022

Keywords

• nonn
• fini
• full

Examples

			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 * * *     * * * * * * *     * * * * * * *
     * * * * *         * * * * *         * * * * *         * * * * *
       * * *             * * *             * * *             * * *
		

Links

• Sander G. Huisman, Mathematica program for this sequence

Crossrefs

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