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A237686 The number of P-positions in the game of Nim with up to four piles, allowing for piles of zero, such that the total number of objects in all piles doesn't exceed 2n. 5
1, 7, 14, 50, 63, 105, 148, 364, 413, 491, 546, 798, 883, 1141, 1400, 2696, 2961, 3255, 3382, 3850, 3983, 4313, 4620, 6132, 6469, 6979, 7322, 8870, 9387, 10941, 12496, 20272, 21833, 23423, 23982, 25746, 26167, 26929, 27524, 30332, 30933 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Partial sums of A237711.
LINKS
T. Khovanova and J. Xiong, Nim Fractals, arXiv:1405.594291 [math.CO] (2014), p. 16 and J. Int. Seq. 17 (2014) # 14.7.8.
FORMULA
a(2n+1) = 7a(n) + a(n-1), a(2n+2) = a(n+1) + 7a(n).
EXAMPLE
There is a position (0,0,0,0) with a total of zero. There are 6 positions with a total of 2 that are permutations of (0,0,1,1). Therefore, a(1)=7.
MATHEMATICA
Table[Length[
Select[Flatten[
Table[{n, k, j, BitXor[n, k, j]}, {n, 0, a}, {k, 0, a}, {j, 0,
a}], 2], Total[#] <= a &]], {a, 0, 100, 2}]
CROSSREFS
Cf. A237711 (first differences), A130665 (3 piles), A238147 (5 piles), A241522, A241718.
Sequence in context: A374509 A045759 A166637 * A170918 A033650 A135536
KEYWORD
nonn
AUTHOR
Tanya Khovanova and Joshua Xiong, May 02 2014
STATUS
approved

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Last modified July 14 05:06 EDT 2024. Contains 374291 sequences. (Running on oeis4.)