The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A241522 The number of P-positions in the game of Nim with up to 4 piles, allowing for piles of zero, such that the number of objects in each pile does not exceed n. 5
 1, 8, 21, 64, 89, 168, 301, 512, 561, 712, 965, 1344, 1801, 2408, 3165, 4096, 4193, 4488, 4981, 5696, 6585, 7720, 9101, 10752, 12433, 14408, 16677, 19264, 22121, 25320, 28861, 32768, 32961, 33544, 34517, 35904, 37657, 39848, 42477, 45568, 48881, 52680, 56965, 61760, 67017 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS P-positions in the game of Nim are tuples of numbers with a Nim-Sum equal to zero. (0,1,1,0) is considered different from (1,0,1,0). Partial sums of A241718. LINKS Table of n, a(n) for n=0..44. Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Identities and periodic oscillations of divide-and-conquer recurrences splitting at half, arXiv:2210.10968 [cs.DS], 2022, pp. 42-43. T. Khovanova and J. Xiong, Nim Fractals, arXiv:1405.594291 [math.CO] (2014), p. 8 and J. Int. Seq. 17 (2014) # 14.7.8. FORMULA If b = floor(log_2(n)) is the number of digits in the binary representation of n and c = n + 1 - 2^b, then a(n) = 2^(3*b) + 6*c^2*2^b + a(c-1). a(2^n-1) = 2^(3*n). EXAMPLE If the largest number is 1, then there should be an even number of piles of size 1. Thus, a(1)=8. MATHEMATICA Table[Length[Select[Flatten[Table[{n, k, j, BitXor[n, k, j]}, {n, 0, a}, {k, 0, a}, {j, 0, a}], 2], #[[4]] <= a &]], {a, 0, 50}] CROSSREFS Cf. A236305 (3 piles), A241523 (5 piles). Cf. A241718 (first differences). Sequence in context: A301538 A192299 A080144 * A096018 A297647 A267144 Adjacent sequences: A241519 A241520 A241521 * A241523 A241524 A241525 KEYWORD nonn AUTHOR Tanya Khovanova and Joshua Xiong, Apr 24 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 6 03:09 EDT 2023. Contains 363138 sequences. (Running on oeis4.)