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A162610 Triangle read by rows in which row n lists n terms, starting with 2n-1, with gaps = n-1 between successive terms.

%I A162610 #18 Apr 09 2020 10:51:36
%S A162610 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,
%T A162610 37,43,49,15,22,29,36,43,50,57,64,17,25,33,41,49,57,65,73,81,19,28,37,
%U A162610 46,55,64,73,82,91,100,21,31,41,51,61,71,81,91,101,111,121
%N A162610 Triangle read by rows in which row n lists n terms, starting with 2n-1, with gaps = n-1 between successive terms.
%C A162610 Note that the last term of the n-th row is the n-th square A000290(n).
%C A162610 Row sums are n*(n^2+2*n-1)/2, apparently in A127736. - _R. J. Mathar_, Jul 20 2009
%H A162610 Harvey P. Dale, <a href="/A162610/b162610.txt">Table of n, a(n) for n = 1..10000</a>
%F A162610 T(n,k) = n+k*n-k, 1<=k<=n. - _R. J. Mathar_, Oct 20 2009
%F A162610 T(n,k) = (k+1)*(n-1)+1. - _Reinhard Zumkeller_, Jan 19 2013
%e A162610 Triangle begins:
%e A162610 1
%e A162610 3, 4
%e A162610 5, 7, 9
%e A162610 7, 10, 13, 16
%e A162610 9, 13, 17, 21, 25
%e A162610 11, 16, 21, 26, 31, 36
%t A162610 Flatten[Table[NestList[#+n-1&,2n-1,n-1], {n,15}]] (* _Harvey P. Dale_, Oct 20 2011 *)
%o A162610 (Python) # From _R. J. Mathar_, Oct 20 2009
%o A162610 def A162610(n, k):
%o A162610     return 2*n-1+(k-1)*(n-1)
%o A162610 print([A162610(n,k) for n in range(1,20) for k in range(1,n+1)])
%o A162610 (Haskell)
%o A162610 a162610 n k = k * n - k + n
%o A162610 a162610_row n = map (a162610 n) [1..n]
%o A162610 a162610_tabl = map a162610_row [1..]
%o A162610 -- _Reinhard Zumkeller_, Jan 19 2013
%Y A162610 Cf. A000027, A000290, A159797, A159798.
%Y A162610 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).
%K A162610 easy,tabl,nonn
%O A162610 1,2
%A A162610 _Omar E. Pol_, Jul 09 2009
%E A162610 More terms from _R. J. Mathar_, Oct 20 2009