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Search: id:A112351
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| A112351 |
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Triangle read by rows, generated from (...5,3,1). |
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1
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| 1, 1, 3, 1, 6, 5, 1, 9, 19, 7, 1, 12, 42, 44, 9, 1, 15, 74, 138, 85, 11, 1, 18, 115, 316, 363, 146, 13, 1, 21, 165, 605, 1059, 819, 231, 15, 1, 24, 224, 1032, 2470, 2984, 1652, 344, 17, 1, 27, 292, 1624, 4974, 8378, 7380, 3060
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OFFSET
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0,3
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COMMENT
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A039755 (Analogues of a Stirling number of the second kind triangle); is generated through an analogous set of operations (but using the matrix M = [1 / 1 3 / 1 3 5 /...]). First few rows of the array are: 1, 3, 5, 7, 9, 11,... 1, 6, 19, 44, 85,... 1, 9, 42, 138, 363,... 1, 12, 74, 316, 1059,... ... Row 2 of the array = A005900 (Octahedral numbers). Row 3 of the array = A061927. First few rows of the triangle are: 1; 1, 3; 1, 6, 5; 1, 9, 19, 7; 1, 12, 42, 44, 9; 1, 15, 74, 138, 85, 11; 1, 18, 115, 316, 363, 146, 13; ...
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FORMULA
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Let M = an infinite lower triangular matrix of the form [1 / 3 1 / 5 3 1 /...] (with the rest of the terms zeros). Perform M^n * [1 0 0 0...] forming an array. Antidiagonals of the array become rows of the triangle A112351.
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EXAMPLE
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The antidiagonal 1 9 19 7 of the array becomes row 3 of the triangle.
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CROSSREFS
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Cf. A039755, A005900, A061927.
Sequence in context: A016575 A116666 A061702 this_sequence A143858 A109954 A153641
Adjacent sequences: A112348 A112349 A112350 this_sequence A112352 A112353 A112354
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 05 2005
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