Search: id:A112737
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%I A112737
%S A112737 1,1,2,8,39,171,719,2757,9751,31312,89927,229614,517854,1022224,1753737,
%T A112737 2598215,3312423,3626632,3413313,2765623,1930324,1160977,600372,265865,
%U A112737 100565,32250,8688,1917,348,50,7,2,0
%N A112737 On the standard 33-hole cross-shaped peg solitaire board, the number 
               of distinct board positions after n jumps (starting with the center 
               vacant).
%C A112737 If symmetry is not taken into account, these numbers are approximately 
               8 times larger (except for those at the start). The sum of this (finite) 
               sequence is 23475688, the total number of distinct board positions 
               that can be reached from the central vacancy on the 33-hole peg solitaire 
               board.
%H A112737 George I. Bell, <a href="http://www.geocities.com/gibell.geo/pegsolitaire/
               EnglishResults.html#jumps">English Peg Solitaire</a>
%H A112737 Bill Butler, <a href="http://www.durangobill.com/Peg33.html">Durango 
               Bill's 33-hole Peg Solitaire</a>
%e A112737 There are four possible first jumps, but they all lead to the same board 
               position (rotationally equivalent), thus a(1)=1.
%Y A112737 Cf. A014225, A014227.
%Y A112737 Sequence in context: A082014 A154133 A077324 this_sequence A162476 A059275 
               A020047
%Y A112737 Adjacent sequences: A112734 A112735 A112736 this_sequence A112738 A112739 
               A112740
%K A112737 full,nonn,fini
%O A112737 0,3
%A A112737 George Bell (gibell(AT)comcast.net), Sep 16 2005

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