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Search: id:A109678
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| A109678 |
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Sequence and first differences include all square numbers exactly once. |
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+0
1
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| 1, 5, 14, 30, 55, 91, 140, 204, 285, 385, 506, 650, 819, 1015, 1240, 1496, 1785, 2109, 2470, 2870, 3311, 3795, 4324, 4900, 5525, 6201, 6930, 7714, 8555, 9455, 10416, 11440, 12529, 13685, 14910, 16206, 17575, 19019, 20540, 22140, 23821, 25585
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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).
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FORMULA
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a(n)=a(n-1)+n^2 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 09 2009]
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EXAMPLE
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Superpose sequence and first differences:
1 5 14 30 55 91 140 204 285 385 506 650 819 1015
.4.9..16..25..36..49...64...81...100...121...144...169...196
All square numbers appear once and only once, either in the sequence itself or in the first differences.
For n=2, a(2)=1+4=5; n=3, a(3)=5+9=14; n=4, a(4)=14+16=30 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 09 2009]
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MAPLE
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seq(sum ((k+1)^2, k=0..n), n=0..41); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 10 2007
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MATHEMATICA
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s = 1; lst = {s}; Do[s += n^2; AppendTo[lst, s], {n, 2, 42, 1}]; lst [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 12 2009]
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CROSSREFS
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Sequence in context: A136135 A096893 A074784 this_sequence A000330 A166068 A070129
Adjacent sequences: A109675 A109676 A109677 this_sequence A109679 A109680 A109681
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KEYWORD
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base,easy,nonn
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AUTHOR
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Eric Angelini (eric.angelini(AT)kntv.be), Aug 30 2005
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