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 A330466 Irregular triangle read by rows: T(n,k) is the number of parts in the partition of n into k consecutive parts that differ by 2, n >= 1, k >= 1, and the first element of column k is in row k^2. 7
 1, 1, 1, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 3, 1, 2, 0, 1, 0, 0, 1, 2, 3, 1, 0, 0, 1, 2, 0, 1, 0, 3, 1, 2, 0, 4, 1, 0, 0, 0, 1, 2, 3, 0, 1, 0, 0, 0, 1, 2, 0, 4, 1, 0, 3, 0, 1, 2, 0, 0, 1, 0, 0, 0, 1, 2, 3, 4, 1, 0, 0, 0, 5, 1, 2, 0, 0, 0, 1, 0, 3, 0, 0, 1, 2, 0, 4, 0, 1, 0, 0, 0, 0, 1, 2, 3, 0, 5, 1, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Since the trivial partition n is counted, so T(n,1) = 1. This is an irregular triangle read by rows: T(n,k), n >= 1, k >= 1, in which column k lists k's interleaved with k-1 zeros, and the first element of column k is in row k^2. Conjecture: row sums give A066839. LINKS FORMULA T(n,k) = k*A303300(n,k). EXAMPLE Triangle begins (rows 1..25): 1; 1; 1; 1, 2; 1, 0; 1, 2; 1, 0; 1, 2; 1, 0, 3; 1, 2, 0; 1, 0, 0; 1, 2, 3; 1, 0, 0; 1, 2, 0; 1, 0, 3; 1, 2, 0, 4; 1, 0, 0, 0; 1, 2, 3, 0; 1, 0, 0, 0; 1, 2, 0, 4; 1, 0, 3, 0; 1, 2, 0, 0; 1, 0, 0, 0; 1, 2, 3, 4; 1, 0, 0, 0, 5; ... For n = 16 there are three partitions of 16 into consecutive parts that differ by 2, including 16 as a partition. They are [16], [9, 7] and [7, 5, 3, 1]. The number of parts of these partitions are 1, 2 and 4 respectively, so the 16th row of the triangle is [1, 2, 0, 4]. CROSSREFS Cf. A000290, A066839, A237048, A303300. Other triangles of the same family are A127093 and A285914. Sequence in context: A286320 A330888 A194525 * A282938 A065368 A010751 Adjacent sequences:  A330463 A330464 A330465 * A330467 A330468 A330469 KEYWORD nonn,tabf AUTHOR Omar E. Pol, Apr 30 2020 STATUS approved

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Last modified August 5 22:41 EDT 2021. Contains 346488 sequences. (Running on oeis4.)