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 A370386 Irregular triangle read by rows. An infinite rooted tree having root node 1 in row n = 0. Nodes in row n each have n + 1 children with values m + k, where m is the value of the parent node and k takes the values of all nodes from the root to the parent including the parent itself. 1
 1, 2, 3, 4, 4, 5, 6, 5, 6, 8, 5, 6, 7, 8, 6, 7, 8, 10, 7, 8, 9, 12, 6, 7, 9, 10, 7, 8, 10, 12, 9, 10, 12, 16, 6, 7, 8, 9, 10, 7, 8, 9, 10, 12, 8, 9, 10, 11, 14, 9, 10, 11, 12, 16, 7, 8, 9, 11, 12, 8, 9, 10, 12, 14, 9, 10, 11, 13, 16, 11, 12, 13, 15, 20, 8, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The paths through the tree represent integer partitions which contain their own first differences and have least part 1. These partitions are counted, including those with any least part, in A364673. LINKS Table of n, a(n) for n=0..75. EXAMPLE Triangle begins: 1; 2; 3, 4; 4, 5, 6, 5, 6, 8; 5, 6, 7, 8, 6, 7, 8, 10, 7, 8, 9, 12, 6, 7, 9, 10, 7, 8, 10, 12, 9, 10, 12, 16; ... The tree starts with root 1 in row n = 0. In row n = 2 the parent node 4 has 3 children using values of k: 1, 2, and 4. Tree begins: row [n] [0] 1 | [1] ____2____ / \ [2] __3__ __4__ / | \ / | \ [3] 4 5 6 5 6 8 PROG (Python) def A370386_rowlist(maxrow): A, C = [[(1, )]], [[1]] for i in range(maxrow): A.append([]) C.append([]) for j in A[i]: for k in j: x = j + (j[-1] + k, ) A[i+1].append(x) C[i+1].append(x[-1]) return(C) CROSSREFS The tree if only distinct values are allowed is A114622. Cf. A000142 (row lengths), A002720 (empirical row sums). Cf. A364673. Sequence in context: A248110 A108872 A147847 * A335572 A268680 A126974 Adjacent sequences: A370383 A370384 A370385 * A370387 A370388 A370389 KEYWORD nonn,easy,tabf AUTHOR John Tyler Rascoe, Feb 28 2024 STATUS approved

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Last modified June 15 11:14 EDT 2024. Contains 373407 sequences. (Running on oeis4.)