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%I #17 Aug 17 2018 11:02:20
%S 0,1,2,1,2,3,2,1,2,3,4,3,4,3,4,3,4,5,4,5,6,5,4,5,4,3,2,3,2,3,4,3,4,5,
%T 4,3,2,3,4,3,2,3,2,1,2,1,2,3,4,3,4,5,4,3,4,3,2,3,2,3,2,3,2,1,2
%N a(n) is the Manhattan distance between n and 1 in a 3-dimensional cubic spiral of positive integers with 1..8 at the center (illustration in the comments).
%C Similar to A214526, but three-dimensional, and the core is 2 X 2 X 2 rather than 1 X 1.
%C The spiral begins as follows:
%C Level z=-2:
%C 95 94 93 92 91 90
%C 96 77 76 75 74 89
%C 97 78 67 66 73 88
%C 98 79 68 65 72 87
%C 99 80 69 70 71 86
%C 100 81 82 83 84 85
%C z=-1:
%C 116 115 114 113 112 111
%C 117 52 51 50 49 110
%C 118 53 62 61 60 109
%C 119 54 63 64 59 108
%C 120 55 56 57 58 107
%C 101 102 103 104 105 106
%C z=0:
%C 137 136 135 134 133 132
%C 138 39 38 37 48 131
%C 139 40 3 2 47 130
%C 140 41 4 1 46 129
%C 121 42 43 44 45 128
%C 122 123 124 125 126 127
%C z=1:
%C 144 145 146 147 148 149
%C 143 34 35 36 25 150
%C 142 33 6 7 26 151
%C 141 32 5 8 27 152
%C 160 31 30 29 28 153
%C 159 158 157 156 155 154
%C z=2:
%C 165 166 167 168 169 170
%C 164 21 22 23 24 171
%C 163 20 11 12 13 172
%C 162 19 10 9 14 173
%C 161 18 17 16 15 174
%C 180 179 178 177 176 175
%C z=3:
%C 186 187 188 189 190 191
%C 185 204 205 206 207 192
%C 184 203 214 215 208 193
%C 183 202 213 216 209 194
%C 182 201 212 211 210 195
%C 181 200 199 198 197 196
%C Algorithm sketch:
%C 1. At every x-y plane the direction is clockwise if z > 0 and counterclockwise if z <= 0.
%C 2. After an N*N cube is complete and we start building an M*M cube, M=N+2:
%C 2a. The spiral at the first new edge of the M*M cube progresses from center to edges, in the same way as the A214526 spiral, e.g., z=-2 in the illustration.
%C 2b. Between the first and last z-edges the spiral progresses according to item 1.
%C 2c. The spiral at the last new edge of the M*M cube progresses from edges to center, e.g., z=3 in the illustration.
%F abs( a(n) - a(n-1) ) = 1.
%Y Cf. A214526.
%K nonn
%O 1,3
%A _Alex Ratushnyak_, Oct 05 2016
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