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Sequence and first differences include all square numbers exactly once.
0

%I #21 Dec 13 2017 02:43:38

%S 1,5,14,30,55,91,140,204,285,385,506,650,819,1015,1240,1496,1785,2109,

%T 2470,2870,3311,3795,4324,4900,5525,6201,6930,7714,8555,9455,10416,

%U 11440,12529,13685,14910,16206,17575,19019,20540,22140,23821,25585

%N Sequence and first differences include all square numbers exactly once.

%C This sequence diverges from A000330 as 4900 (which is 70^2) appears in the sequence itself - thus won't be added to any a(n).

%e Superpose sequence and first differences:

%e 1 5 14 30 55 91 140 204 285 385 506 650 819 1015

%e .4.9..16..25..36..49...64...81...100...121...144...169...196

%e All square numbers appear once and only once, either in the sequence itself or in the first differences.

%K easy,nonn

%O 1,2

%A _Eric Angelini_, Aug 30 2005

%E Two programs removed that were reproducing A000330 and therefore erroneous. - _R. J. Mathar_, Mar 06 2013