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 A173304 Triangle generated from the array in A173302 (partition numbers starting new rows at n = 1, 3, 7, 15, ...). 3
 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 3, 2, 4, 4, 3, 4, 6, 4, 7, 8, 6, 1, 8, 11, 9, 2, 12, 15, 12, 3, 14, 20, 17, 5, 21, 26, 23, 7, 24, 35, 31, 11, 34, 45, 41, 15, 41, 58, 55, 21, 1, 55, 75, 71, 29, 1, 66, 96, 93, 40, 2, 88, 121, 120, 53, 3, 105, 154, 154, 72, 5, 137, 193, 196, 94, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Row sums = A000041, the partition numbers. LINKS Table of n, a(n) for n=0..76. FORMULA The generating array is in A173302. 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, ... 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, ... 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, ... 1, 1, 2, 3, 5, 7, 11, 15, 22, ... 1, ... ... Take finite differences from the bottom, creating a new array in which rows are A002865 (a slight variant), A027336, A027338, A027342, ...; i.e., the numbers of partitions of n that do not contain (1, 2, 4, 8, ...) as a part. EXAMPLE The finite difference array starts: 1, 1, 1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 21, 24, ...; = A002865 (a variant) 1, 1, 2, 3, 4, 6, 8, 11, 15, 20, 26, 35, ...; = A027336 1, 1, 2, 3, 4, 6, 9, 12, 17, 23, 31, ...; = A017338 1, 1, 2, 3, 5, 7, 11, ...; = A027342 ... Last, columns of the array become rows of triangle A173304: 1; 1; 1, 1; 2, 2, 1; 2, 3, 2; 4, 4, 3; 4, 6, 4, 1; 7, 8, 6, 1; 8, 11, 9, 2; 12, 15, 12, 3; 14, 20, 17, 5; 21, 26, 23, 7; 24, 35, 31, 11; 34, 45, 41, 15; 41, 58, 55, 21, 1; 55, 75, 71, 29, 1; 66, 96, 93, 40, 2; 88, 121, 120, 53, 3; 105, 154, 154, 72, 5; 137, 193, 196, 94, 7; ... CROSSREFS Cf. A000041, A173301, A173302, A173303. Sequence in context: A091423 A221914 A264401 * A029251 A263073 A133091 Adjacent sequences: A173301 A173302 A173303 * A173305 A173306 A173307 KEYWORD nonn,tabf,uned AUTHOR Gary W. Adamson, Feb 15 2010 STATUS approved

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Last modified February 24 02:58 EST 2024. Contains 370288 sequences. (Running on oeis4.)