

A237686


The number of Ppositions 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 doesn't exceed 2n.


5



1, 7, 14, 50, 63, 105, 148, 364, 413, 491, 546, 798, 883, 1141, 1400, 2696, 2961, 3255, 3382, 3850, 3983, 4313, 4620, 6132, 6469, 6979, 7322, 8870, 9387, 10941, 12496, 20272, 21833, 23423, 23982, 25746, 26167, 26929, 27524, 30332, 30933
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OFFSET

0,2


COMMENTS



LINKS



FORMULA

a(2n+1) = 7a(n) + a(n1), a(2n+2) = a(n+1) + 7a(n).


EXAMPLE

There is a position (0,0,0,0) with a total of zero. There are 6 positions with a total of 2 that are permutations of (0,0,1,1). Therefore, a(1)=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



KEYWORD

nonn


AUTHOR



STATUS

approved



