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A238759 The number of P-positions in the game of Nim with up to five piles, allowing for piles of zero, such that the total number of objects in all piles is 2n. 2
1, 10, 15, 100, 65, 150, 175, 1000, 565, 650, 475, 1500, 925, 1750, 1875, 10000, 5565, 5650, 3475, 6500, 3725, 4750, 3875, 15000, 8425, 9250, 6375, 17500, 10625, 18750, 19375, 100000, 55565, 55650, 33475, 56500, 31725, 34750, 23875, 65000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

First differences of A238147.

LINKS

Table of n, a(n) for n=0..39.

T. Khovanova and J. Xiong, Nim Fractals, arXiv:1405.594291 [math.CO] (2014), p. 17 and J. Int. Seq. 17 (2014) # 14.7.8.

FORMULA

a(2n+1) = 10*a(n), a(2n+2) = a(n+1) + 5*a(n).

EXAMPLE

The P-positions with the total of 4 are permutations of (0,0,0,2,2) and (0,1,1,1,1). Therefore, a(2)=15.

MATHEMATICA

Table[Length[

  Select[Flatten[

    Table[{n, k, j, i, BitXor[n, k, j, i]}, {n, 0, a}, {k, 0, a}, {j,

      0, a}, {i, 0, a}], 3], Total[#] == a &]], {a, 0, 90, 2}]

(* Second program: *)

(* b = A238147 *) b[n_] := b[n] = Which[n <= 1, {1, 11}[[n+1]], OddQ[n], 11 b[(n-1)/2] + 5 b[(n-1)/2 - 1], EvenQ[n], b[(n-2)/2 + 1] + 15 b[(n-2)/2]];

Join[{1}, Differences[Array[b, 40, 0]]] (* Jean-Fran├žois Alcover, Dec 14 2018 *)

CROSSREFS

Cf. A238147 (partial sums), A048883 (3 piles), A237711 (4 piles), A241523, A241731.

Sequence in context: A056522 A056511 A166626 * A278349 A114703 A134515

Adjacent sequences:  A238756 A238757 A238758 * A238760 A238761 A238762

KEYWORD

nonn

AUTHOR

Tanya Khovanova and Joshua Xiong, May 02 2014

STATUS

approved

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Last modified October 1 15:55 EDT 2020. Contains 337443 sequences. (Running on oeis4.)