A001966 v-pile counts for the 4-Wythoff game with i=2. (Formerly M1739 N0689)

2, 7, 13, 18, 23, 28, 34, 39, 44, 49, 54, 60, 65, 70, 75, 81, 86, 91, 96, 102, 107, 112, 117, 123, 128, 133, 138, 143, 149, 154, 159, 164, 170, 175, 180, 185, 191, 196, 201, 206, 212, 217, 222, 227, 233, 238, 243, 248, 253, 259, 264, 269, 274, 280, 285, 290

Offset

0,1

Comments

See Connell (1959) for further information.

References

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

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

Links

T. D. Noe, Table of n, a(n) for n = 0..10000

Ian G. Connell, A generalization of Wythoff's game, Canad. Math. Bull. 2 (1959) 181-190

N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence).

Formula

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

A bisection of A001950: a(n) = A001950(2*n+1). - N. J. A. Sloane, Mar 16 2021

a(n) = A001965(n)+4*n+2. - Chai Wah Wu, Aug 25 2022

Mathematica

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

Prog

(Python)
from math import isqrt
def A001966(n): return ((m:=(n<<1)+1)+isqrt(5*m**2)>>1)+m # Chai Wah Wu, Aug 25 2022

Crossrefs

Cf. A001965 (u-pile), A001950.

Sequence in context: A106911 A019370 A356107 * A209886 A168465 A140562

Adjacent sequences: A001963 A001964 A001965 * A001967 A001968 A001969

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Edited by Hugo Pfoertner, Dec 27 2021

Status

approved