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%I #6 Jan 27 2014 12:58:14
%S 1,1,2,2,3,3,4,3,2,3,2,3,4,5,6,5,6,7,5,4,3,9,4,3,4,5,6,10,5,6,7,8,9,8,
%T 7,6,10,11,12,6,5,4,5,6,7,4,5,6,7,8,9,10,12,11,10,10,11,12,13,14,9,8,
%U 7,6,5,6,17,18,6,5,6,7,8,9,10,11,16,15,9,10,11,12
%N Manhattan distances between n and 2*n in a left-aligned triangle with next M natural numbers in row M: 1, 2 3, 4 5 6, 7 8 9 10, etc.
%e Triangle in which we find distances begins:
%e _1
%e _2 3
%e _4 5 6
%e _7 8 9 10
%e 11 12 13 14 15
%e 16 17 18 19 20 21
%e 22 23 24 25 26 27 28
%e 29 30 31 32 33 34 35 36
%e 37 38 39 40 41 42 43 44 45
%o (Python)
%o import math
%o def getXY(n):
%o y = int(math.sqrt(n*2))
%o if n<=y*(y+1)/2: y-=1
%o x = n - y*(y+1)/2
%o return x, y
%o for n in range(1,88):
%o ox, oy = getXY(n)
%o nx, ny = getXY(2*n)
%o print str(abs(nx-ox)+abs(ny-oy))+',',
%Y Cf. A232113, A236345, A236346.
%K nonn
%O 1,3
%A _Alex Ratushnyak_, Jan 23 2014
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