A131421 Triangle read by rows (n>=1, 1<=k<=n): T(n,k) = 2*(n+k) - 3.

1, 3, 5, 5, 7, 9, 7, 9, 11, 13, 9, 11, 13, 15, 17, 11, 13, 15, 17, 19, 21, 13, 15, 17, 19, 21, 23, 25, 15, 17, 19, 21, 23, 25, 27, 29, 17, 19, 21, 23, 25, 27, 29, 31, 33, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41

Offset: 1

Author

Gary W. Adamson, Jul 10 2007

Keywords

• nonn
• tabl
• easy

Comments

Row sums = A000567, the octagonal numbers: (1, 8, 21, 40, 65, 96,...).

Examples

			First few rows of the triangle are:
1;
3, 5;
5, 7, 9;
7, 9, 11, 13;
9, 11, 13, 15, 17;
11, 13, 15, 17, 19, 21;
13, 15, 17, 19, 21, 23, 25;
...
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows 1 <= n <= 150).

Crossrefs

Cf. A127775, A000567.

Programs

Mathematica

Table[2 (n + k) - 3, {n, 150}, {k, n}] // Flatten (* Michael De Vlieger, Oct 06 2017 *)

PARI

tabl(nn) = {ma = matrix(nn, nn, n, k, (k<=n)); mb = matrix(nn, nn, n, k, (2*n - 1)*(k==n)); mr = ma*mb + mb*ma - ma; for (n = 1, nn, for (k = 1, n, print1(mr[n, k], ", ");); print(););} \\ Michel Marcus, Mar 04 2014

Formula

(A000012 * A127775) + (A127775 * A000012) - A000012, where all the sequences and the result are interpreted as infinite lower triangular matrices.

Extensions

Corrected and extended by Michel Marcus, Mar 04 2014

New name from Andrey Zabolotskiy, Oct 06 2017