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

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

Offset

1,2

Comments

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

Links

Harvey P. Dale, Table of n, a(n) for n = 1..10000

Formula

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

Example

Triangle begins:
1
3, 4
5, 7, 9
7, 10, 13, 16
9, 13, 17, 21, 25
11, 16, 21, 26, 31, 36

Mathematica

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

Prog

(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

Crossrefs

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

Keyword

easy,tabl,nonn

Author

Omar E. Pol, Jul 09 2009

Extensions

More terms from R. J. Mathar, Oct 20 2009

Status

approved