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A131421 Triangle read by rows (n>=1, 1<=k<=n): T(n,k) = 2*(n+k) - 3. 1
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

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

FORMULA

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

EXAMPLE

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;

...

MATHEMATICA

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

PROG

(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

CROSSREFS

Cf. A127775, A000567.

Sequence in context: A195990 A023840 A276501 * A088743 A219844 A168056

Adjacent sequences:  A131418 A131419 A131420 * A131422 A131423 A131424

KEYWORD

nonn,tabl,easy

AUTHOR

Gary W. Adamson, Jul 10 2007

EXTENSIONS

Corrected and extended by Michel Marcus, Mar 04 2014

New name from Andrey Zabolotskiy, Oct 06 2017

STATUS

approved

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Last modified October 16 11:11 EDT 2019. Contains 328056 sequences. (Running on oeis4.)