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

%I

%S 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,

%T 23,25,15,17,19,21,23,25,27,29,17,19,21,23,25,27,29,31,33,19,21,23,25,

%U 27,29,31,33,35,37,21,23,25,27,29,31,33,35,37,39,41

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

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

%H Michael De Vlieger, <a href="/A131421/b131421.txt">Table of n, a(n) for n = 1..11325</a> (rows 1 <= n <= 150).

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

%e First few rows of the triangle are:

%e 1;

%e 3, 5;

%e 5, 7, 9;

%e 7, 9, 11, 13;

%e 9, 11, 13, 15, 17;

%e 11, 13, 15, 17, 19, 21;

%e 13, 15, 17, 19, 21, 23, 25;

%e ...

%t Table[2 (n + k) - 3, {n, 150}, {k, n}] // Flatten (* _Michael De Vlieger_, Oct 06 2017 *)

%o (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

%Y Cf. A127775, A000567.

%K nonn,tabl,easy

%O 1,2

%A _Gary W. Adamson_, Jul 10 2007

%E Corrected and extended by _Michel Marcus_, Mar 04 2014

%E New name from _Andrey Zabolotskiy_, Oct 06 2017

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Last modified August 8 06:27 EDT 2020. Contains 336290 sequences. (Running on oeis4.)