

A238147


The number of Ppositions 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
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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(n1), 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[(n1)/2] + 5 a[(n1)/2  1], EvenQ[n], a[(n2)/2 + 1] + 15*a[(n2)/2]];
Array[a, 34, 0] (* JeanFrançois 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



