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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. 20

%I #18 Apr 09 2020 10:51:36

%S 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 37,43,49,15,22,29,36,43,50,57,64,17,25,33,41,49,57,65,73,81,19,28,37,

%U 46,55,64,73,82,91,100,21,31,41,51,61,71,81,91,101,111,121

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

%C Note that the last term of the n-th row is the n-th square A000290(n).

%C Row sums are n*(n^2+2*n-1)/2, apparently in A127736. - _R. J. Mathar_, Jul 20 2009

%H Harvey P. Dale, <a href="/A162610/b162610.txt">Table of n, a(n) for n = 1..10000</a>

%F T(n,k) = n+k*n-k, 1<=k<=n. - _R. J. Mathar_, Oct 20 2009

%F T(n,k) = (k+1)*(n-1)+1. - _Reinhard Zumkeller_, Jan 19 2013

%e Triangle begins:

%e 1

%e 3, 4

%e 5, 7, 9

%e 7, 10, 13, 16

%e 9, 13, 17, 21, 25

%e 11, 16, 21, 26, 31, 36

%t Flatten[Table[NestList[#+n-1&,2n-1,n-1], {n,15}]] (* _Harvey P. Dale_, Oct 20 2011 *)

%o (Python) # From _R. J. Mathar_, Oct 20 2009

%o def A162610(n, k):

%o return 2*n-1+(k-1)*(n-1)

%o print([A162610(n,k) for n in range(1,20) for k in range(1,n+1)])

%o (Haskell)

%o a162610 n k = k * n - k + n

%o a162610_row n = map (a162610 n) [1..n]

%o a162610_tabl = map a162610_row [1..]

%o -- _Reinhard Zumkeller_, Jan 19 2013

%Y Cf. A000027, A000290, A159797, A159798.

%Y 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 easy,tabl,nonn

%O 1,2

%A _Omar E. Pol_, Jul 09 2009

%E More terms from _R. J. Mathar_, Oct 20 2009

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