A238759 - OEIS

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.

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-François Alcover, Dec 14 2018 *)

CROSSREFS

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

Sequence in context: A056511 A339314 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