

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



FORMULA



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



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



KEYWORD



AUTHOR



EXTENSIONS



STATUS

approved



