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Search: id:A122053
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| A122053 |
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Triangle read by rows, based on Chebyshev polynomials of the first kind: T[n,x]=(-2+4*x)*T[n-1,x]-T[n-2,x]. |
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+0
1
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| -3, 5, 1, -7, 1, 169, 9, 1, 985, 8721, -11, 1, 5741, 86329, 489061, 13, 1, 33461, 854569, 6811741, 31622993, -15, 1, 195025, 8459361, 94875313, 567451585, 2351330961, 17, 1, 1136689, 83739041, 1321442641, 10182505537, 51622180721, 198710804449, -19, 1, 6625109, 828931049, 18405321661
(list; table; graph; listen)
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OFFSET
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1,1
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REFERENCES
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Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964, 9th Printing (1970), pp. 782.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].
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FORMULA
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a(n,m) = (-2 + 4*m)a(n - 1) - p(n - 2)
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EXAMPLE
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-3
5, 1
-7, 1, 169
9, 1, 985, 8721
-11, 1, 5741, 86329, 489061
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MATHEMATICA
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p[n_] := p[n] = Cancel[Simplify[(-2 + 4*x)p[n - 1] - p[n - 2]]]; p[ -2] = 1; p[ -1] = 1; a = Table[Table[p[n], {x, 0, n}], {n, 0, 10}] Flatten[a]
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CROSSREFS
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Cf. A115066.
Adjacent sequences: A122050 A122051 A122052 this_sequence A122054 A122055 A122056
Sequence in context: A065077 A118788 A028510 this_sequence A124084 A133045 A114216
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KEYWORD
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sign,tabl,uned
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 13 2006
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