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Search: id:A096164
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| A096164 |
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Triangle relating to Chebyshev polynomials, companion to A039598. |
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1
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| 1, 2, 1, 5, 4, 1, 12, 14, 6, 1, 30, 44, 27, 8, 1, 74, 133, 104, 44, 10, 1, 185, 388, 369, 200, 65, 12, 1, 460, 1110, 1236, 814, 340, 90, 14, 1
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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A039598 = A038207 * A053121. The non-commutativity property of the matrix products generates two companion matrices: A039598 and A096164. Check: using (Y,Z), Y*Z generates the first 4 rows of A096164, but Z*Y = [1 0 0 0 / 2 1 0 0 / 5 4 1 0 / 14 14 6 1], (having the first 4 rows of A039598). Row sums of A039598 = A001700: 1, 3, 10, 35, 126, 462, 1716...; but row sums of A096164 = 1, 3, 10, 33, 110, 336, 1220, 4065... Diagonal terms under 2, 4, 6...= A014106: 5, 14, 27, 44, 65, 90...
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FORMULA
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A096164 = A053121 * A038207 = A053121 * (A007318)^2; where A053121, A038207 and A007318 are (respectively): infinite lower triangular matrices of the Catalan triangle (with zeros), Pascal's triangle and Pascal's triangle squared.
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EXAMPLE
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Using 4 X 4 matrices from A053121 and A038207: [1 0 0 0 / 0 1 0 0 / 1 0 1 0 / 0 2 0 1] = Y; [1 0 0 0 / 2 1 0 0 / 4 4 1 0 / 8 12 6 1]= Z. Then Y*Z = [1 0 0 0 / 2 1 0 0 / 5 4 1 0 / 12 14 6 1]. Delete the zeros getting the first 4 rows of A096164.
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CROSSREFS
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Cf. A039598, A007318, A038207, A053121, A001700, A049310.
Sequence in context: A129161 A103415 A054456 this_sequence A104710 A039598 A128738
Adjacent sequences: A096161 A096162 A096163 this_sequence A096165 A096166 A096167
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KEYWORD
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nonn,uned,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 19 2004
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