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%I #14 Dec 02 2016 01:13:53
%S 1,3,2,6,7,4,10,9,5,8,15,16,11,17,12,21,20,14,19,13,18,28,29,22,30,23,
%T 31,24,36,35,27,34,26,33,25,32,45,46,37,47,38,48,39,49,40,55,54,44,53,
%U 43,52,42,51,41,50,66,67,56,68,57,69,58,70,59,71,60,78,77,65,76,64,75
%N Square table, read by antidiagonals, of least distinct positive integers such that the sum of any two consecutive terms in any row is a square number.
%C A permutation of the natural numbers.
%F T(0, k) = (k+1)*(k+2)/2 for k>=0, T(n, 0) = floor((n+1)^2/2) for n>0, T(n, k+1) = (2*floor((n+1)/2) + k+1)^2 - T(n, k) for n>0 and k>=0.
%e Table begins:
%e 1 3 6 10 15 21 28 36 45 55 66 ...
%e 2 7 9 16 20 29 35 46 54 67 77 ...
%e 4 5 11 14 22 27 37 44 56 65 79 ...
%e 8 17 19 30 34 47 53 68 76 93 103 ...
%e 12 13 23 26 38 43 57 64 80 89 107 ...
%e 18 31 33 48 52 69 75 94 102 123 133 ...
%e 24 25 39 42 58 63 81 88 108 117 139 ...
%e 32 49 51 70 74 95 101 124 132 157 167 ...
%e 40 41 59 62 82 87 109 116 140 149 175 ...
%e 50 71 73 96 100 125 131 158 166 195 205 ...
%e 60 61 83 86 110 115 141 148 176 185 215 ...
%e 72 97 99 126 130 159 165 196 204 237 247 ...
%Y Cf. A083363 (diagonal), A083364 (antidiagonal sums).
%Y Cf. A000217 (1st row), A080476 (1st column).
%K nonn,tabl,nice
%O 0,2
%A _Paul D. Hanna_, Apr 27 2003
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