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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
Sequence in context: A195990 A023840 A276501 * A088743 A219844 A168056
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 April 23 19:56 EDT 2024. Contains 371916 sequences. (Running on oeis4.)