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A158405
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Triangle T(n,m) = 1+2*m of odd numbers read along rows, 0<=m<n.
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19
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1, 1, 3, 1, 3, 5, 1, 3, 5, 7, 1, 3, 5, 7, 9, 1, 3, 5, 7, 9, 11, 1, 3, 5, 7, 9, 11, 13, 1, 3, 5, 7, 9, 11, 13, 15, 1, 3, 5, 7, 9, 11, 13, 15, 17, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23
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OFFSET
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1,3
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COMMENTS
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The triangle sums, see A180662 for their definitions, link this triangle of odd numbers with seventeen different sequences, see the crossrefs. The knight sums Kn14 - Kn110 have been added. - Johannes W. Meijer, Sep 22 2010
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LINKS
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FORMULA
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a(n) = 2*i-1, where i = n-t(t+1)/2, t = floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Feb 03 2013
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EXAMPLE
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The triangle contains the first n odd numbers in row n:
1;
1,3;
1,3,5;
1,3,5,7;
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0| (= 0)
1| 1 = 1/3 * ( 3) (= 1)
2| 1 + 3 = 1/3 * ( 5 + 7) (= 4)
3| 1 + 3 + 5 = 1/3 * ( 7 + 9 + 11) (= 9)
4| 1 + 3 + 5 + 7 = 1/3 * ( 9 + 11 + 13 + 15) (= 16)
5| 1 + 3 + 5 + 7 + 9 = 1/3 * (11 + 13 + 15 + 17 + 19) (= 25)
(End)
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MATHEMATICA
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PROG
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(Haskell)
a158405 n k = a158405_row n !! (k-1)
a158405_row n = a158405_tabl !! (n-1)
a158405_tabl = map reverse a099375_tabl
(PARI) a(n) = 2*(n-floor((-1+sqrt(8*n-7))/2)*(floor((-1+sqrt(8*n-7))/2)+1)/2)-1;
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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