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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 April 23 19:56 EDT 2024. Contains 371916 sequences. (Running on oeis4.)