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 A352499 Irregular triangle read by rows: T(n,k) is the sum of all parts of the partition of n into consecutive parts that contains 2*k-1 parts, and the first element of the column k is in row A000384(k). 3
 1, 2, 3, 4, 5, 6, 6, 7, 0, 8, 0, 9, 9, 10, 0, 11, 0, 12, 12, 13, 0, 14, 0, 15, 15, 15, 16, 0, 0, 17, 0, 0, 18, 18, 0, 19, 0, 0, 20, 0, 20, 21, 21, 0, 22, 0, 0, 23, 0, 0, 24, 24, 0, 25, 0, 25, 26, 0, 0, 27, 27, 0, 28, 0, 0, 28, 29, 0, 0, 0, 30, 30, 30, 0, 31, 0, 0, 0, 32, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This triangle is formed from the odd-indexed columns of the triangle A285891. LINKS FORMULA T(n,k) = n*A351824(n,k). EXAMPLE Triangle begins: 1; 2; 3; 4; 5; 6, 6; 7, 0; 8, 0; 9, 9; 10, 0; 11, 0; 12, 12; 13, 0; 14, 0; 15, 15, 15; 16, 0, 0; 17, 0, 0; 18, 18, 0; 19, 0, 0; 20, 0, 20; 21, 21, 0; 22, 0, 0; 23, 0, 0; 24, 24, 0; 25, 0, 25; 26, 0, 0; 27, 27, 0; 28, 0, 0, 28; ... For n = 21 the partitions of 21 into on odd number of consecutive parts are [21] and [8, 7, 6], so T(21,1) = 1 and T(21,2) = 8 + 7 + 6 = 21. There is no partition of 21 into five consecutive parts so T(21,3) = 0. CROSSREFS Row sums give A352257. Row n has A351846(n) terms. The number of nonzero terms in row n equals A082647(n). Cf. A000384, A237048, A245579, A285891, A299765, A351824, A352425. Sequence in context: A069754 A097622 A236561 * A110010 A091987 A357149 Adjacent sequences: A352496 A352497 A352498 * A352500 A352501 A352502 KEYWORD nonn,tabf AUTHOR Omar E. Pol, Mar 19 2022 STATUS approved

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Last modified March 30 09:17 EDT 2023. Contains 361609 sequences. (Running on oeis4.)