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A159797
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Triangle read by rows in which row n lists n+1 terms, starting with n, such that the difference between successive terms is equal to n-1.
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33
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0, 1, 1, 2, 3, 4, 3, 5, 7, 9, 4, 7, 10, 13, 16, 5, 9, 13, 17, 21, 25, 6, 11, 16, 21, 26, 31, 36, 7, 13, 19, 25, 31, 37, 43, 49, 8, 15, 22, 29, 36, 43, 50, 57, 64, 9, 17, 25, 33, 41, 49, 57, 65, 73, 81, 10, 19, 28, 37, 46, 55, 64, 73, 82, 91, 100, 11, 21, 31, 41, 51, 61, 71, 81, 91, 101
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Note that the last term of the n-th row is the n-th square A000290(n).
See also A162611, A162614 and A162622.
The triangle sums, see A180662 for their definitions, link the triangle A159797 with eleven sequences, see the crossrefs. [From Johannes W. Meijer, May 20 2011]
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LINKS
| David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS
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FORMULA
| Given m = floor( (sqrt(8*n+1)-1)/2 ), then a(n) = m + (n - m*(m+1)/2)*(m-1) [From Carl R. White (oeisfan(AT)phodd.net), Jul 24 2010]
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EXAMPLE
| Triangle begins:
0;
1, 1;
2, 3, 4;
3, 5, 7, 9;
4, 7,10,13,16;
5, 9,13,17,21,25;
6,11,16,21,26,31,36;
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MAPLE
| A159797:=proc(n) local m: m := floor( (sqrt(8*n+1)-1)/2 ): A159797(n):= m + (n - m*(m+1)/2)*(m-1) end: seq(A159797(n), n=0..75); [From Johannes W. Meijer, May 20 2011]
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PROG
| (Other) /*GNU bc*/ scale=0; for(n=0; n<76; n++){m=(sqrt(8*n+1)-1)/2; print m+(n-m*(m+1)/2)*(m-1), ", "}; print"\n" [From Carl R. White (oeisfan(AT)phodd.net), Jul 24 2010]
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CROSSREFS
| Cf. A000290, A001477, A081493, A159798, A162609, A162610, A162611, A162614, A162622.
Cf.: A006002 (row sums). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 17 2009]
Cf. A163282, A163283, A163284, A163285. [From Omar E. Pol (info(AT)polprimos.com), Nov 18 2009]
From Johannes W. Meijer, May 20 2011: (Start)
Triangle sums (see the comments): A006002 (Row1), A050187 (Row2), A058187 (Related to Kn11, Kn12, Kn13, Fi1 and Ze1), A006918 (Related to Kn21, Kn22, Kn23, Fi2 and Ze2), A000330 (Kn3), A016061 (Kn4), A190717 (Related to Ca1 and Ze3), A144677 (Related to Ca2 and Ze4), A000292 (Related to Ca3, Ca4, Gi3 and Gi4) A190718 (Related to Gi1) and A144678 (Related to Gi2). (End)
Sequence in context: A141128 A160180 A078908 * A152920 A080383 A086369
Adjacent sequences: A159794 A159795 A159796 * A159798 A159799 A159800
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Omar E. Pol (info(AT)polprimos.com), Jul 09 2009
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EXTENSIONS
| Edited by Omar E. Pol (info(AT)polprimos.com), Jul 18 2009
More terms from Omar E. Pol (info(AT)polprimos.com), Nov 18 2009
More terms from Carl R. White (oeisfan(AT)phodd.net), Jul 24 2010
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