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%I M0647 #21 Aug 26 2019 15:54:58
%S 1,2,3,5,7,10,14,20,30,45,69,104,157,236,356,540,821,1252,1908,2909,
%T 4434,6762,10319,15755,24066,36766,56176,85837,131172,200471,306410,
%U 468371,715975,1094516,1673232,2557997,3910683
%N Numbers of Twopins positions.
%C The complete sequence by _R. K. Guy_ in "Anyone for Twopins?" starts with a(0) = 0, a(1) = 1, a(2) = 1, a(3) = 1 and a(4) =1. The formula for a(n) confirms these values. - _Johannes W. Meijer_, Aug 24 2013
%D R. K. Guy, ``Anyone for Twopins?,'' in D. A. Klarner, editor, The Mathematical Gardner. Prindle, Weber and Schmidt, Boston, 1981, pp. 2-15.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H R. K. Guy, <a href="/A005251/a005251_1.pdf">Anyone for Twopins?</a>, in D. A. Klarner, editor, The Mathematical Gardner. Prindle, Weber and Schmidt, Boston, 1981, pp. 2-15. [Annotated scanned copy, with permission]
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1,2,-2,0,0,0,-1).
%F G.f.: (x^5*(1-x^2+x^3-2*x^5-x^6-x^7-x^8-x^9))/((1-x^2-x^5)*(1-2*x+x^2-x^5)). - _Ralf Stephan_, Apr 22 2004
%F a(n) = sum(A102541(n-k-1, 2*k), k=0..floor((n-1)/3)), n >= 5. - _Johannes W. Meijer_, Aug 24 2013
%t LinearRecurrence[{2,0,-2,1,2,-2,0,0,0,-1},{1,2,3,5,7,10,14,20,30,45},40] (* _Harvey P. Dale_, Aug 26 2019 *)
%K nonn,easy
%O 5,2
%A _N. J. A. Sloane_.
%E More terms from _Johannes W. Meijer_, Aug 24 2013
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