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A238147 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 doesn't exceed 2n. 2
1, 11, 26, 126, 191, 341, 516, 1516, 2081, 2731, 3206, 4706, 5631, 7381, 9256, 19256, 24821, 30471, 33946, 40446, 44171, 48921, 52796, 67796, 76221, 85471, 91846, 109346, 119971, 138721, 158096, 258096, 313661, 369311 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Partial sums of A238759.

LINKS

Table of n, a(n) for n=0..33.

T. Khovanova and J. Xiong, Nim Fractals, arXiv:1405.594291 [math.CO] (2014), p. 18 and J. Int. Seq. 17 (2014) # 14.7.8.

FORMULA

a(2n+1) = 11a(n) + 5a(n-1), a(2n+2) = a(n+1) + 15a(n).

EXAMPLE

There is 1 position (0,0,0,0,0) with a total of zero. There are 10 positions with a total of 2 that are permutations of (0,0,0,1,1). Therefore, a(1)=11.

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], #[[5]] <= a &]], {a, 0, 35}]

(* Second program: *)

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

Array[a, 34, 0] (* Jean-François Alcover, Dec 14 2018 *)

CROSSREFS

Cf. A238759 (first differences), A130665 (3 piles), A237686 (4 piles), A241523, A241731.

Sequence in context: A046806 A224197 A027521 * A137014 A137013 A014468

Adjacent sequences:  A238144 A238145 A238146 * A238148 A238149 A238150

KEYWORD

nonn

AUTHOR

Tanya Khovanova and Joshua Xiong, May 02 2014

STATUS

approved

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Last modified October 23 08:40 EDT 2021. Contains 348211 sequences. (Running on oeis4.)