A001966 - OEIS

%I M1739 N0689 #34 Aug 26 2022 05:35:49

%S 2,7,13,18,23,28,34,39,44,49,54,60,65,70,75,81,86,91,96,102,107,112,

%T 117,123,128,133,138,143,149,154,159,164,170,175,180,185,191,196,201,

%U 206,212,217,222,227,233,238,243,248,253,259,264,269,274,280,285,290

%N v-pile counts for the 4-Wythoff game with i=2.

%C See Connell (1959) for further information.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A001966/b001966.txt">Table of n, a(n) for n = 0..10000</a>

%H Ian G. Connell, <a href="http://dx.doi.org/10.4153/CMB-1959-024-3">A generalization of Wythoff's game</a>, Canad. Math. Bull. 2 (1959) 181-190

%H N. J. A. Sloane, <a href="/A115004/a115004.txt">Families of Essentially Identical Sequences</a>, Mar 24 2021 (Includes this sequence).

%F a(n) = floor( (n+1/2)*(3+sqrt 5) ).

%F A bisection of A001950: a(n) = A001950(2*n+1). - _N. J. A. Sloane_, Mar 16 2021

%F a(n) = A001965(n)+4*n+2. - _Chai Wah Wu_, Aug 25 2022

%t Table[Floor[(n + 1/2)*(Sqrt[5] + 3)], {n, 0, 100}] (* _T. D. Noe_, Aug 17 2012 *)

%o (Python)

%o from math import isqrt

%o def A001966(n): return ((m:=(n<<1)+1)+isqrt(5*m**2)>>1)+m # _Chai Wah Wu_, Aug 25 2022

%Y Cf. A001965 (u-pile), A001950.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_

%E Edited by _Hugo Pfoertner_, Dec 27 2021