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 A237711 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 is 2n. 10
 1, 6, 7, 36, 13, 42, 43, 216, 49, 78, 55, 252, 85, 258, 259, 1296, 265, 294, 127, 468, 133, 330, 307, 1512, 337, 510, 343, 1548, 517, 1554, 1555, 7776, 1561, 1590, 559, 1764, 421, 762, 595, 2808, 601, 798, 463, 1980, 637, 1842, 1819, 9072, 1849 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS First differences of A237686. 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) = 6a(n), a(2n+2) = a(n+1) + a(n). G.f.: Product_{k>=0} (1 + 6*x^(2^k) + x^(2^(k+1))). - Ilya Gutkovskiy, Mar 16 2021 EXAMPLE The P-positions with the total of 4 are permutations of (0,0,2,2) and (1,1,1,1). Therefore, a(2)=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. A237686 (partial sums), A048883 (3 piles), A238759 (5 piles), A241522, A241718. Sequence in context: A159582 A041553 A047190 * A033043 A037411 A025626 Adjacent sequences:  A237708 A237709 A237710 * A237712 A237713 A237714 KEYWORD nonn AUTHOR Tanya Khovanova and Joshua Xiong, May 02 2014 STATUS approved

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Last modified July 29 07:28 EDT 2021. Contains 346340 sequences. (Running on oeis4.)