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A162610
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Triangle read by rows in which row n lists n terms, starting with 2n-1, with gaps = n-1 between successive terms.
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20
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1, 3, 4, 5, 7, 9, 7, 10, 13, 16, 9, 13, 17, 21, 25, 11, 16, 21, 26, 31, 36, 13, 19, 25, 31, 37, 43, 49, 15, 22, 29, 36, 43, 50, 57, 64, 17, 25, 33, 41, 49, 57, 65, 73, 81, 19, 28, 37, 46, 55, 64, 73, 82, 91, 100, 21, 31, 41, 51, 61, 71, 81, 91, 101, 111, 121
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Note that the last term of the n-th row is the n-th square A000290(n).
Row sums are n*(n^2+2*n-1)/2, apparently in A127736. - R. J. Mathar, Jul 20 2009
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 1..10000
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FORMULA
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T(n,k) = n+k*n-k, 1<=k<=n. - R. J. Mathar, Oct 20 2009
T(n,k) = (k+1)*(n-1)+1. - Reinhard Zumkeller, Jan 19 2013
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EXAMPLE
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Triangle begins:
1
3, 4
5, 7, 9
7, 10, 13, 16
9, 13, 17, 21, 25
11, 16, 21, 26, 31, 36
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MATHEMATICA
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Flatten[Table[NestList[#+n-1&, 2n-1, n-1], {n, 15}]] (* Harvey P. Dale, Oct 20 2011 *)
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PROG
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(Python) # From R. J. Mathar, Oct 20 2009
def A162610(n, k):
return 2*n-1+(k-1)*(n-1)
print([A162610(n, k) for n in range(1, 20) for k in range(1, n+1)])
(Haskell)
a162610 n k = k * n - k + n
a162610_row n = map (a162610 n) [1..n]
a162610_tabl = map a162610_row [1..]
-- Reinhard Zumkeller, Jan 19 2013
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CROSSREFS
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Cf. A000027, A000290, A159797, A159798.
Cf. A209297; A005408 (left edge), A000290 (right edge), A127736 (row sums), A056220 (central terms), A026741 (number of odd terms per row), A142150 (number of even terms per row), A221491 (number of primes per row).
Sequence in context: A174269 A112882 A180152 * A155935 A081606 A079945
Adjacent sequences: A162607 A162608 A162609 * A162611 A162612 A162613
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KEYWORD
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easy,tabl,nonn
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AUTHOR
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Omar E. Pol, Jul 09 2009
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EXTENSIONS
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More terms from R. J. Mathar, Oct 20 2009
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STATUS
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approved
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