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Search: id:A136159
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| A136159 |
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A Chebyshev polynomial triangle of the first kind defined by T(n+1,x) = 3x*T(n,x) - T(n-1,x). |
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+0
2
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| 1, 1, 3, -1, 9, -4, 17, -15, 1, 81, -54, 7, 143, -189, 36, -1, 729, -648, 162, -10, 2187, -2187, 675, -66, 1
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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The triangle is defined by the recurrence relations: T(0,x) = 1 T(1,x) = x T(n+1,x) = 3x*T(n,x) - T(n-1,x). Row sums(unsigned) = A003688 starting (1, 1, 4, 13, 43, 142, 469,...).
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FORMULA
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A generating function = (l - tx)/(1 - 3tx + t^2). Given triangle A136158, shift down columns to allow for (1, 1, 2, 2, 3, 3,...) terns in each row.
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EXAMPLE
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First few rows of the polynomials are:
1;
x;
3x^2 - 1;
9x^3 - 4x;
27x^4 - 15x^2 + 1;
81x^5 - 54x^3 + 7x;
243x^6 - 189x^4 + 36x^2 - 1;
729x^7 - 648x^5 + 162x^3 - 10x;
...
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CROSSREFS
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Cf. A136158, A003688.
Adjacent sequences: A136156 A136157 A136158 this_sequence A136160 A136161 A136162
Sequence in context: A124573 A127550 A021317 this_sequence A091579 A005533 A112626
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KEYWORD
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tabl,sign
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 16 2007
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