

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
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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



