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%I #21 Jun 14 2020 09:44:32
%S 0,1,0,2,3,0,3,1,2,0,4,2,3,15,0,5,12,1,5,12,0,6,15,8,10,4,9,0,7,13,10,
%T 1,8,14,11,0,8,14,11,14,13,7,13,10,0,9,4,9,4,1,15,6,15,6,0,10,7,12,11,
%U 9,6,7,5,11,8,0,11,5,14,2,5,1,12,3,13,12,7
%N Array read by upward antidiagonals: T(n,k) (n >= 0, k > 0) = nim-division of n by k.
%C This is the array A334290 with a leading row of 0's.
%H <a href="/index/Ni#Nimmult">Index entries for sequences related to Nim-multiplication</a>
%F T(n, k) = A051775(n, A051917(k)).
%F T(n, 1) = n.
%F T(1, n) = A051917(k).
%F T(n, n) = 1.
%e The array begins:
%e n\k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
%e ---+------------------------------------------------------------
%e 0| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e 1| 1 3 2 15 12 9 11 10 6 8 7 5 14 13 4 --> A051917(n)
%e 2| 2 1 3 5 4 14 13 15 11 12 9 10 7 6 8
%e 3| 3 2 1 10 8 7 6 5 13 4 14 15 9 11 12
%e 4| 4 12 8 1 13 15 7 3 14 11 10 2 5 9 6
%e 5| 5 15 10 14 1 6 12 9 8 3 13 7 11 4 2
%e 6| 6 13 11 4 9 1 10 12 5 7 3 8 2 15 14
%e 7| 7 14 9 11 5 8 1 6 3 15 4 13 12 2 10
%e 8| 8 4 12 2 6 5 9 1 7 13 15 3 10 14 11
%e 9| 9 7 14 13 10 12 2 11 1 5 8 6 4 3 15
%e 10| 10 5 15 7 2 11 4 14 12 1 6 9 13 8 3
%e 11| 11 6 13 8 14 2 15 4 10 9 1 12 3 5 7
%e 12| 12 8 4 3 11 10 14 2 9 6 5 1 15 7 13
%e 13| 13 11 6 12 7 3 5 8 15 14 2 4 1 10 9
%e 14| 14 9 7 6 15 4 3 13 2 10 12 11 8 1 5
%e 15| 15 10 5 9 3 13 8 7 4 2 11 14 6 12 1
%e | | | | |
%e | | | | A004474(n)
%e | | | A004477(n)
%e | | A004480(n)
%e | A006015(n)
%e A004468(n)
%Y Cf. A004468, A004474, A004477, A004480, A006015, A051775, A051776, A051917, A334290.
%K nonn,tabl
%O 0,4
%A _Rémy Sigrist_, Jun 13 2020